The experienced centre-back seems like a surplus to requirements at Stamford Bridge.
He’s been a skilful player in west London since joining from Bolton in 2012 but his better years are arguably like a past to him.
Fulham have been related with a move, but Rosenior isn’t convinced he’ll want to make the short move to Craven Cottage.
“Gary Cahill’s been mentioned who would be a tremendous signing for Fulham,” he told Love Sport Radio.
“I don’t know if he would go there.
“But someone like that who would go in there and dominate the back four or back three, and tell them when they’re out of possession.
“That’s when you find your position on the pitch, when you’re out of possession it makes sure you’re concentrating.
“I look at the Fulham team, when they’re out of possession they’re a couple of yards off here and a couple of yards off there, and it’s causing them all sorts of problems. That’s what they need, a big character in the heart of that defence.
He’s had stronger characters around him.
“He became captain when Terry moved on, so obviously he’s a leader.
“I honestly believe coaches can do so much in terms of getting players to defend better.”
Fulham have conceded 49 goals this term – the worst in the Premier League.