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 morning, but it was rejected and Spurs do not want to let the 29-year-old go.
"I wouldn't want to let him go. He is a good player," manager Harry Redknapp said. "I brought him on for the last 10 minutes against Everton on Wednesday and he didn't give the ball away."
Redknapp added: "I don't have any need to weaken the squad. I would rather have a good squad for last 18 matches of the season than let one or two go who could play a part in the run-in."
Pienaar has started just five league games for Spurs since moving to White Hart Lane from Everton, where he was a fans' favourite.
He has been linked with a return to Goodison Park on loan for the rest of the season and Aston Villa have also been mentioned as possible suitors.
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.
He suffered a concussion after clashing heads with team-mate Bongani Khumalo in February and picked up a niggling groin problem towards the end of last season.
He was confident the problem had gone away, but it flared up again in pre-season and he had to undergo surgery as a result, ruling him out until mid-September before another two setbacks kept him sidelined until November and he has struggled to make an impact since.
Source: PA
Source: PA