The midfielder agreed to the mutual termination of his contract with Besiktas in August and has recently been training with former club Arsenal.
While reports claimed that Oxlade-Chamberlain was keen to remain close to his family, sources close to the player have told Herald Sport that talks with Celtic are positive and progressing well.
O’Neill plans to revisit the matter when he returns to his desk after travelling back from Aberdeen after last night’s scheduled Premiership clash was postponed by a waterlogged pitch.
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The deadline to register a squad for forthcoming Europa League knockout tie with VfB Stuttgart is midnight on Thursday. With time short, it remains to be seen whether a deal might be rushed through in time to bring Oxlade-Chamberlain in to the equation.
The Parkhead club completed the capture of Junior Adamu, Joel Mvuka and Benjamin Arthur before the signing deadline on Monday night.
And O’Neill is keen to add Oxlade-Chamberlain’s experience to his options, saying: “He could play midfield for us easily. Is he one of those players who could go past players on the outside wide? I wouldn’t be sure. But he could do a job.”
The cancellation of last night’s Pittodrie clash was blamed by Aberdeen on “prolonged rain over the last few weeks”, Celtic returning to third place in the Premiership after Rangers secured a thumping 5-1 win over ten man Kilmarnock.