The 32-year-old is thought to be growing increasingly worried about his future at White Hart Lane with American Kasey Keller pushing very hard for the number one jersey.
It has been reported that Sullivan has a clause in his contract that allows him to move on, if Spurs receive a bid of £1 million and that could very well tempt Rangers into making a move.
However, Alex McLeish's outfit already have German ace Stefan Klos at the club, so Sullivan would be walking out of one battle in North London into an equally hard battle for the number one post in Glasgow.
It remains to be seen whether Sullivan does decide to stay or whether he feels his future lies away Tottenham.
