Currently training with the English Premier League leaders after spending last season with Turkish giants Besiktas, O'Neill has held positive discussions with the 32-year-old, who is currently a free agent.
"I have spoken to him," said the Celtic manager. "Obviously I had a look at what he was doing in Turkey and it was fine. He was playing in a more withdrawn role, I think Ole Gunnar Solskjaer was out there and asked if he would help in that sort of position.
"You don’t lose ability. You might lose a bit of hunger, but he was definitely up for it. He was up for a challenge. At 32 years of age he’s still got it. He will have other options. He is training at Arsenal and Arsenal have had a few injuries so they might even take him on.
"But he knew about the club, he had spoken to Joe Hart, that was just by chance or a coincidence. I’m not saying he spoke to Joe Hart two days ago, it might have been months ago. But it was fine. He lives down in London.
"It’s not the money, it’s not for the money. I really left it. I didn’t progress any further, yet. It was only 24, 36 hours ago."
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"He could play midfield for us, easily," O'Neill continued. "Is he one of those players who could go past the players on the outside, wide? I wouldn’t be sure. But he could do a job.
"When I signed James Milner from Newcastle to Aston Villa, James was wide right hand side and I know that position very well because I played it and I knew falls and the concerns you have out there when you’re wide, taking someone on, looking for a bit of help to play one-twos and stuff but James could play there.
"I think he (Oxlade-Chamberlain) had heard of me. Maybe his grandad told him about me!
"If it doesn’t materialise, we have good players in here at this minute. But I’d love to have him at the end of the day. I think in time getting into matchday mode, I don’t think that would be a major problem. If you can get a player of that sort of calibre, that would be great. It would be really great. But I can understand that there are lots of other things around there. Arsenal too.
"Listen, if we were even on a close list that would be fine. The main thing would be has he still got the desire, which I believe he has. I still believe he’s young enough."
With Oxlade-Chamberlain potentially coming into strengthen Celtic's engine room for the run-in, the club managed to retain one of its key midfield cogs in January despite late transfer interest from Nottingham Forest. Indeed, Forest are believed to have made three bids for Arne Engels, the last of which reached £25million with future add-ons. All were rejected.
"The things were coming in and the board were keeping me informed," said O'Neill. "But they never came to me and said what are your thoughts. I just assumed they would know what my thoughts were.
"It’s difficult to turn that down and also it’s something the player would at least double or treble his wages. But he seemed bright enough and breezy this morning.
"We all talk about statements from football clubs and half the time I don’t believe it but I do think it is, because that’s big. To turn down that at this stage in January is really, really big. The consequences of that is really big. I never asked how they were making it up but let’s say it was £20m with £5m added-on and that was attainable, you’re talking about £25m and that is big.
"But coming at the stage that it did, it didn't give us any time, anyway, let me put it this way, to look at that sort of player."
Arne Engels (Image: Shutterstock)
In total, Celtic made five January signings: Julian Araujo, Tomas Cvancara, Junior Adamu, Joel Mvuka, and Benjamin Arthur. Johnny Kenny, Hayato Inamura, and Shin Yamada aside, they lost no one of note. O'Neill is glad to have a settled squad for the coming fight.
"We had a meeting in this very room here about half-past ten, quarter to eleven," he said. "And it's just nice, the boys are in the room now, competition for places, a bit of a battle on, which is good for a start. And two, people can't do anything now until the summer. So that's it. And it's a bit of a relief for me in that aspect.
"Who knows? Rangers and Hearts may have signed better players at the end of the day. I don't know. I'm happy with what we've done, and I'm going to get on with it, really, and just try it. And even if it's possible, which I think I can do, I think maybe I can try and improve the players - even the ones that we're bringing in."
After leapfrogging Rangers into second over the weekend, Celtic travel to face Aberdeen at Pittodrie on Wednesday evening as they continue to chase down William Hill Premiership leaders Heart of Midlothian.
"It's great credit to Hearts and what they've done," O'Neill said. "Absolutely. Really great credit. And, you know, they're asking about stories... I think what the manager has done at Falkirk, they caused us all sorts of problems down there. They came with freedom there on Sunday. And for us, I knew that energy would be down a bit after Thursday night. So those are the sort of things.
"So a few people coming in to help us here along the way, and even some of the lads who haven't played regularly in their own teams, I think that should give us a bit of freshness. That's what I'm hoping for."
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The pressure on Celtic's new signings to come in and perform mid-title race could not be greater. Are they aware of what they have gotten themselves into? "If they don't, they soon will, O'Neill said. "Usually at this stage of the season, you're in a good position in the league and stuff like this here. It's not the case this time. We're chasing it down.
"We can, honestly. I know that old cliched phrase, we can only, we can really only look after ourselves now."
Oxlade-Chamberlain aside, the sole focus for Celtic between now and May lies on the pitch. Still alive in Europe, very much in the title fight, and eager to win the Scottish Cup, O'Neill is glad that he doesn't have to worry about transfers anymore.
"I'm actually quite pleased it's over, really I am," he said of the January window. "Scrummaging around, trying to get players that you think can improve the squad, and improve it a lot, hence us trying to buy some players here that I think would suit the football club for the foreseeable future.
"When it happens, when those things didn't materialise, yeah, fine. But I've been in it. Not recently, obviously, but during my time, January transfer windows, there's a similarity about things, you know, that takes place."
O'Neill expects to hear from Oxlade-Chamberlain's camp in the next 24 to 48 hours. Arsenal manager Mikel Arteta recently refused to rule out signing the midfielder on a short-term deal as he continues to train with the North London club.