But Rovers have again made enquiries about signing the 29-year-old.
Hull manager Peter Taylor said: "Ian (Atkins) 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 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."