The 31-year-old is available to leave the club, but has turned down moves to the only interested parties so fat.
"A few clubs have asked about Steve Guinan's availability but at the moment he's staying put with us," Robins boss John Ward told the Gloucestershire Echo.
"One or two clubs' names have been put to Steve but he has said 'no, I am staying here'. He's entitled to do that and I respect that decision."