The Turkish club have made four offers for the 27-year old, having seen them all rejected, and SunSport suggests that he is fairly certain to remain at Ibrox.
Whittaker's deal at 'Gers expires at the end of next season but manager Ally McCoist is reportedly confident of keeping the Scotland international, who according to Bursa transfer director Erkan Kamat, is set to depart Glasgow.
"We want to bring Whittaker to our training camp as soon as possible," he said.
"We've agreed a deal in principle with him and need to reach agreement with Rangers. I expect him to sign this week."