The Parkhead midfielder believes the transfer might actually happen.
The duo are good friends after years of playing together at Liverpool, with whom they won the Premier League in 2020.
Having recently joined Celtic as a free agent, Oxlade-Chamberlain is keen to see Scotland captain Robertson also make the move.
Robertson, a boyhood fan of Celtic, was in the club's academy. His contract with Liverpool expires this summer.
Oxlade-Chamberlain revealed his thoughts on the possible transfer during an appearance on the Celtic Podcast.
The midfielder said: "We’re very close with Robbo and his family, his mum and dad.
"We were next door neighbours for years and years.
"I knew all about Celtic and Glasgow from them for years.
"Robbo makes no secret of what he thinks about this club so when I was linked he was the first one to call me and said get yourself up there now."
"I just said to him ‘it’s a shame you’re not here with me.’"
"He might join me soon.
"I’d hope to see him here one day.
"I think he’d be amazing."
The bonds between Oxlade-Chamberlain and Robertson run deep, with their connection extending to their partners and children as well.
He added: "I’m obviously really close with Robbo and his missus and the kids, and my missus is really close with them also.
"We get on really well with them.
"So having him as a reference point was perfect for me."
Oxlade-Chamberlain made it quite clear the role Robertson played in his move to Glasgow and settling in the city.
His inside knowledge of Celtic and the local area, courtesy of the Scotland national team captain, was crucial in his transition.
Oxlade-Chamberlain shared a few more details.
"He told me where I need to live, where I need to go, he’s told me everything.
"He’s a proper Glasgow boy."
The rapport between the two players offers a glimpse into the camaraderie, often unseen, between top-flight footballers.
It also serves as a reminder of the personal dimensions that can play into professional decisions such as transfers.
The potential reunion of Oxlade-Chamberlain and Robertson at a club dear to both of them would certainly be an exciting development for Celtic fans.
It remains to be seen whether Robertson, at the peak of his career, will indeed make the move to Scotland.
With his deep-rooted connections to Celtic and assistance in Oxlade-Chamberlain's move, the situation is certainly an interesting one to watch.