So far they have failed in their pursuit of the 27-year old Scotland international but reports suggest that one final attempt will be made as they believe Whittaker wants to link up with former 'Gers teammate Kenny Miller.
Bursaspor's director of transfers, Erkan Kamat, insists the club will again go for Whittaker and if they are unsuccessful will focus on other defenders.
"Whittaker wants to come to Turkey, there is no problem with him," he told the Daily Record.
"But every time we contact Rangers with a new offer we are told the same - (Ally) McCoist doesn't want to sell him. We have made persistent offers.
"This situation cannot go on so we'll give Rangers one more chance to sell. If not, we move to other targets."