The 31-year-old, who departed Craven Cottage at the end of last season, is currently training with the Championship outfit.
"He's still here training with us. We've made him an offer and it's up to Chris really whether he wants to take it," Redknapp told Sky Sports News.
"I think we need to know pretty soon. He can sign after the deadline because he's out of work, but we need an answer."
A number of Championship clubs are also believed to be monitoring proceedings.