The winger joined Spurs from Everton a year ago but has failed to break in to the first team, partly due to a series of injuries.
It is understood new Rangers boss Mark Hughes made a bid for the South African on Friday, but it was rejected and Spurs do not want to let the 29-year-old go.
Frustrated: Steven Pienaar (left) has had a bit-part role at Spurs
Pienaar's Spurs career started promisingly, with the South African slotting in to the team after an injury to Gareth Bale last season.
He started the Londoners' Champions League second-round game at AC Milan but a series of injuries meant he saw less first-team action.