The 29-year-old is yet to play for the Scottish Championship side this season.
The Scottish Sun reports that the 29-year-old has one more year left on his contract at Ibrox, but it appears that Mark Warburton may not stand in his way if a suitable bid comes in from one of the interested clubs.
Although Bell started his career with the Light Blues as the club's first choice, injuries saw him lose his place for the majority of last season, while the arrival of Wes Foderingham in the summer has meant that he has failed to make a single appearance for the Gers this term, even in the cup competitions.
And with The Scottish Sun claiming that Warburton is already on the lookout for another goalkeeper, it seems unlikely that Bell will see his future with his current side if he falls even further down the pecking order.
The Scottish Sun adds that a move to one of the Scottish sides reportedly chasing his signature would depend on whether they are playing in the top flight next season. But with Bell beginning his career at Rugby Park, it is perhaps Killie that have the advantage, although Bristol City's promising second half of the season may also make them an attractive option to the stopper.