Shaw will be in the spotlight this weekend as City hope to add to their WSL crown with an FA Cup trophy.
They travel to Stamford Bridge on Sunday (15:30 BST) to face Chelsea in the semi-finals, with the winner playing either Liverpool or Brighton at Wembley on 18 May.
But Chelsea manager Sonia Bompastor gave no hints as to Shaw’s future when asked about it on Thursday.
“I’m seeing reports of big players being linked to Chelsea and that’s normal,” she said.
“We are ambitious and we want to have a lot of top players in our team. Bunny Shaw is playing for City so it’s not for me to comment on.”
Asked if Shaw would be on Bompastor’s personal wishlist, she added: “Who wouldn’t have her on their personal wishlist? Someone crazy maybe!
“But again, I think we need to be respectful, as Bunny is playing for City this season. She is a great player, for sure.”
The Blues boss was also “sure” Chelsea will have “an ambitious team” next season and emphasised her confidence in the club to recruit well.
Reports suggest they are ready to pay Shaw up to £1m a year and Bompastor admitted signing a number nine is high on the club’s priority list.
“Yeah, if you analyse our season, some of the games we played, especially in the first half of the season, we didn’t have Sam Kerr back fully fit to perform with us, Aggie Beever-Jones was struggling with injuries and we didn’t have Mayra Ramirez for the full season,” she added.
“If you compare that to Manchester City, Arsenal and even Manchester United, and you ask them to play without their number nine or top scorer, I think it would have been completely different for them.
“That is our reality. We know at this level, for Chelsea, it is really important to have a number nine who is performing, playing fully fit and is available.”