Shaw looks set to leave City this summer after talks stalled over a new contract.
Chelsea, who won six titles in a row before City’s recent success, are favourites to sign Shaw, who previously had no desire to leave the club.
But a breakdown in communications led to her exploring other options and Chelsea are understood to have offered at least one more year on a contract than City were willing to agree to.
Reports suggest Chelsea are ready to pay Shaw up to £1m a year and while boss Sonia Bompastor gave no hint as to whether Shaw’s future lying with the club, she admitted in a news conference on Thursday that signing a number nine is high on the Blues’ priority list.
Speaking on Friday, City manager Andree Jeglertz said: “I still hope she’s signing a new contract with Manchester City, definitely, but that’s more of a discussion for the player and for people at the club.
“Right now, the most important thing is to enjoy our player, and she’s here to compete with us, and do everything she can.”
City face Chelsea in the FA Cup semi-finals on Sunday (15:30 BST), with the winner playing either Liverpool or Brighton at Wembley on 31 May.