"They have fancied each other for ages but have never been single at the same time before," a source told the Mirror. "Kelly thinks Gethin could definitely be boyfriend material."
Another insider added, "Gethin thinks Kelly is gorgeous. He can't believe his luck, and he'd like this to become more serious."
Kelly split from on-off boyfriend Danny Cipriani, 26, in August amid reports of his infidelity.
However, her rumoured romance with Gethin, 35, could complicate her friendship with classical singer Katherine Jenkins, who was previously engaged to the handsome Daybreak presenter.
Gethin and Katherine ended their relationship in 2011 after four years together.
Kelly and Gethin, meanwhile, have been friends for a number of years, ever since they both competed in series five of Strictly Come Dancing in 2007.
Kelly recently admitted she wished she had stayed away from relationships until she was in her thirties.
Asked by the Sunday Mirror what advice she would give her younger self, she replied, "Stay away from relationships. I did everything the wrong way round. I should probably have stayed single until now and focused on myself a lot more."
The beautiful brunette, whose past boyfriends include Jason Statham, Billy Zane and Thom Evans, added, "When I look back, I think, 'Oh my gosh, I could have spent that time focusing on myself so much more.'"