Kermode was tipped to replace former presenter Jonathan Ross, despite repeatedly denying any link with the programme and telling Radio 5 Live last week that he did not have the "mainstream sensibility" required for the show.
Winkleman told The Times: "I think [Mark] didn't want it because he said himself they'd go for someone more mainstream.
"It's not just going to be me on there. There will be other, brilliant - not that I'm not brilliant - film critics, all kinds of fantastic people, really clever film people. Different, exciting guests. I'd love him to be there."
Regarding her salary for the show, she added: "I'm on much, much, much, much, much, much less than you'd think. I'd pay them, I really would.
"When I met with the producers they said that I'd probably have to go to two screenings a day. I felt like the luckiest person on the planet."
It has been suggested that Winkleman will receive under £200,000 per series for the show and will have to give up her Golden Globes presenting job for Sky.
> Winkleman wants to prove doubters wrong