While Rovers boss Sean O'Driscoll has every confidence in young keeper Ben Smith, 20, he admits he would sign Sullivan if it was possible.
The former Scottish international is currently playing in the Leeds first team due to an injury suffered by Graham Stack.
"We have declared an interest if Neil's situation changes at Leeds," said O'Driscoll. "If something comes up long-term that we felt was in the best interests of the club, like a Neil Sullivan, he would be a good mentor for Ben. We know that Ben is capable of playing in the first team but he has got years ahead of him in the game."