The 20-year-old spent 18 months on loan at the Glasgow club before returning to Manchester City at the end of last season.
Roberts has been linked with a move to French club Nice but, ahead of Tuesday night’s Betfred Cup last-16 tie against Kilmarnock at Celtic Park, Davies insisted the Scottish champions still retain hope.
“They have been talking and the situation is always open to a certain extent because the transfer window is still open,” Davies said.
“Patrick is someone we really enjoyed working with and there is obviously always going to be home here for Patrick if that suits everybody.
“The exact situation for Pat and Man City will be between him and the club at the moment.
“All I know is we value and rate the player and I am sure that if is right for everybody then something will be done, but we can’t really control that at the moment.
“There is constant dialogue really.
“He has been involved in games and stuff with Manchester City but it is not too dissimilar to other players and agents we talk to and keep in touch with.
“That’s a normal process, not just with Pat.
“He his playing for Manchester City so I can’t comment too much on it.
“All I can tell you from my side and speaking for the manager is how much we enjoyed working with him and the rest will take care of itself.”