The Turkish left-back has had a slower than expected start to his Ibrox career having made just three apperances since joining for a £3.4million fee – potentially rising to £5million with add-ons – from Besiktas in the summer.
Yilmaz has six international caps to his name and has played over 50 times for Besiktas but he has been unable to claim the left-back berth from Borna Barisic, who has remained first-choice despite his own inconsistent form.
While unlikely to be handed a start against Hearts at Tynecastle on Saturday, Van Bronckhorst hinted his summer recruit could feature more in the coming weeks after noting some positive steps being taken both on and off the training field.
“For Ridvan this is a new club in a new country,” the Rangers boss said. “He is settling in really well.
"In the beginning it was a bit hard for him to get settled but I see improvement in his training and also in his behaviour. He is more settled in with the players so for me that is always good to see.
"We have to see in the coming weeks that he will feature more in the team, depending on his training sessions and also what we need in games.”