Potters bid for Fortune
The 21-year-old stopper was the subject of two recent bids from Preston North Bid - both of which were rejected by the West Country outfit.
Robins player-manager Brian Tinnion (pictured) is keen to keep the former Tottenham Hotspur trainee, who signed with the League One club back in March 2001.
The youngster has struggled to get regular first team action at Ashton Gate, with the likes of Tony Butler and Danny Coles commanding the club's rearguard last season.
Fortune has been tipped to make the breakthrough this season, but City look like they have a real fight on their hands to keep hold of the young stopper.
Meanwhile, Stoke have signed four of their youngster to new contracts at The Britannia Stadium.
Gareth Owen, Andy Wilkinson, Ben Foster and Jay Denny have agreed fresh terms with the Midlands club.
Wilkinson, meanwhile, will be starting the season on loan with Scottish First Division side Partick Thistle.