The 32-year-old midfielder will be out of contract at the end of the season and has been linked with a move away from the Etihad.
Pep Guardiola is in favour of keeping him at the club and Manchester City are open to offering him a new contract.
Gundogan has remained a big part of the team but his future at the club remains very much up in the air.
And according to German broadcaster Sky Deutschland, a decision on whether to sign a new deal has not been taken.
Gundogan is still weighing up his options but it will also be a personal decision as much as a professional one.
He is set to become a father in the coming days and the situation of his family will be taken into account on whether he will stay in England.
The midfielder will wait until taking a final call but he has not ruled out leaving Manchester City yet.
Barcelona recently met his agent and are considering snapping him up on a free transfer in the summer.