The Belgian has under a year to run on his current deal, meaning at present he can leave for free next summer.
The midfielder very nearly joined Juventus on transfer deadline day, while Everton and Stoke made offers for the player in July.
But now, according to Izvestia, Zenit are trying to persuade Witsel to stay put and sign a new deal.
The Russian club were reluctant to sell the 27-year-old in the summer as they struggled to find an adequate replacement.
Zenit still believe they will struggle to snap up a player equal to Witsel’s ability and as a result they are now determined to keep him.