The ex-England international has been clubless since leaving Turkish side Besiktas last year.
O'Neill, speaking before Celtic's match against Aberdeen, discussed the potential move for the 32-year-old.
He said: "I do like him. He has been training at Arsenal since his time in Turkey."
The Celtic manager revealed he has spoken to Oxlade-Chamberlain and is aware of his various options, including those nearer to London.
O'Neill showed keen interest in securing a deal, expressing surprise at the lack of existing offers for the free agent midfielder.
He added: "I'd be very interested in doing a deal, but as I said, I'm surprised teams haven't already teed him up.
"As he's been training with Arsenal for a considerable length of time, while it's not match fitness, he is fit - but he's got loads of options."
Oxlade-Chamberlain has most notably played for Arsenal and Liverpool.