The 32-year-old has been training with former club Arsenal after mutually terminating his contract with Besiktas in August and despite reports that he could slide into the Gunners squad, he looks to be making a move much further North.
Celtic boss Martin O’Neill has added Julian Araujo, Tomas Cvancara, Junior Adamu, Joel Mvuka and Benjamin Arthur to his side during the winter window but is reportedly in talks to snap up Oxlade-Chamberlain.
This comes from The Sun and The Express, who state that advanced talks have commenced and the former England star is ready to make the switch in the coming days.
The Scottish champions are confident of completing the signing as he prepares for a medical, which is set to take place today.
Reports had indicated he preferred to remain close to London following the birth of his second child, but a chance to sign for Celtic could be too hard to pass up as he plans to move his family further up the UK.
O'Neill is a fan
Asked if the 35-times capped England player was someone he liked, O’Neill stated: "I do. I genuinely do. Yes. He has trained at Arsenal for some time since his time in Turkey.
"In terms of fitness, it's not match fitness, but it's fine. We'll see. And listen, he's got loads of options.
"I think he was very excited about what we were saying. He knows about the football club. He's a big friend of Joe Hart and Joe's spoken to him. Not on our behalf. It was just a conversation with Joe."