According to the Evening Standard, City are hoping to get an extension sorted for their 32-year-old skipper.
Kompany is out of contract in the summer.
And Pep Guardiola would like him to renew.
"We are considering it, we are talking about that," Guardiola is quoted as saying by the Evening Standard.
"I would like it. he's our captain, 11 years here.
"He's one of the best central defenders I've ever seen."