However, City manager Peter Taylor has revealed that talks with his counterpart in Bristol, Ian Atkins, are resuming.
"Ian did contact me at the end of the season to ask about Jamie and I think there have been some discussions.
"I said I didn't have a problem with Jamie talking to them and at the end of the day he has to work out what is best for him.
"I think Bristol are prepared to give him a two-year deal and he's only under contract to us for another 12 months.
"On top of that, they want him to play first-team football which is something I can't guarantee him if he stops here."
Taylor is already on the lookout to sign a striker as cover for Ben Burgess who faces a lengthy lay-off with cruciate ligament damage to his knee. If he's without Forrester as well then he may look to make another signing, otherwise Danny Allsopp, Jon Walters and Stuart Elliott would be his only available forwards.