The striker, who was cynically hacked down by Stoke's Ryan Shawcross two weeks ago, has seen various specialists regarding his ankle injury.
The former Everton and Arsenal striker was initially thought to miss three months but the ligament damage is a bit worse than first feared.
Owls physio Mark Palmer told the club's official site: "Franny has been seeing a surgeon over the last couple of weeks after his scans, which confirmed serious ankle ligament damage on both sides of his ankle, which is slightly unusual.
"We will rehabilitate him for around six to eight weeks and if Franny is tolerating that well and the ankle is stable, then we can push on from there.
"We've put a time frame of around three to four months on his return."
Richard Wood meanwhile, who dislocated his shoulder against