The French defender, a target for Arsenal, has declared he could be on the move.
But Forster told BILD: "In Stuttgart he is an untouched regular player, is set in central defence. I recommend him to confirm his services for another year.
"He is still so young, you do not need to hurry now."
He added: "Pavard must remember that he will enter through his World Cup participation late in preseason. This complicates the familiarisation for a young player in a big club."