His contract will expire at the end of the season and there are rumours that he might be returning back to England.
The 31-year-old joined Matsatsantsa in 2015 and has enjoyed a trophy-laden spell with the Tshwane team.
SuperSport Chief Executive Officer Stan Matthews has expressed the desire to keep him for one more season.
The Bafana Bafana international was born in Cape Town, but left SA at the age of six. He played for Scottish giants Rangers and English Premiership giants Chelsea F.C. when he was still young.
He also played in the English lower leagues for Oldham Athletic and Doncaster Rovers before joining Matsatsantsa. He says he will not join another PSL club.
SuperSport have won two MTN 8 trophies and two Nedbank Cup trophies, and also reached the CAF Confederation Cup final in 2017, but lost to TP Mazembe from the Democratic Republic of Congo.
They are currently third on the PSL log trailing log leaders Kaizer Chiefs by 13 points. Furman says they will push Amakhosi all the way to the finishing line.
-Report by Vincent Sitsula