Forsyth's future on the BBC One reality show has been the source of much tabloid speculation over recent years, but following his knighthood in June, rumours that he may be considering leaving the show have become more rampant.
Ex-Strictly champion and TV presenter Hollins has thrown his hat into the ring as a possible replacement for the Generation Game TV legend.
"Do you know what, I would love to do that. That would be a dream come true," Hollins told Digital Spy.
"Not only to follow in Sir Brucie's footsteps - he's a big hero of mine - but just to host one of the best shows on telly. Of course, I'd love it."
Hollins, who will return to BBC One next month in daytime TV series Dirty Tricks of the Tradesmen, claimed that Strictly was very much still an integral part of his life.
"When September comes around, I go from being a sports journalist to being a dancer," he said.
"I'll never ever get sick of talking about Strictly Come Dancing though. It is and was an amazing programme to work on. I loved every single second of it and wish I could do it all over again. But it's time for everyone else to have a go.
"It is still very weird though when people ask me things like, 'How good a dancer do you think Edwina Currie will be?' How on Earth would I know? Those questions come up all the time now."
Hollins won Strictly two years ago with professional dance partner Ola Jordan, but admitted that he had concerns about Jordan's new celebrity partner Robbie Savage.
Hollins said: "They've had footballers in the past like Peter Shilton and John Barnes. The trouble is that they are very athletic, but they are not necessarily aesthetically pleasing.
"That's the problem for sportsmen. You can handle the training, but to dance in an aesthetically pleasing way is really tricky. You can train all you want, but you can end up running around like a rhino."
Joking about Savage's notorious temperament on the football pitch might translate to the dancefloor, Hollins said: "There may be a few bookable offences, but hopefully he'll embrace it.
"He's the sort of brilliant character that the show needs and thrives off. A character who will confront the judges, but who could also be a great dancer."
Strictly Come Dancing returns tonight at 9pm on BBC One.
Watch Chris Hollins dancing the Charleston with Ola Jordan below: