The quizzer - nicknamed The Beast - is reportedly in talks to join this year's line up.
6ft 6in Mark, who recently showed off his two-stone weight loss, could take to the dancefloor come the autumn.
"Mark has become one of the best-known personalities on TV so he has come on to Strictly’s radar," a source told the Daily Mirror newspaper. “They think he could be a real hit with viewers, as he has been on The Chase.
“He would certainly make people stand up and take notice with his stature.”
And the insider claimed: "They’re eyeing him up as the comedy character – like Rev Richard Coles last year and Ed Balls the year before.”
Another name rumoured for the new series of Strictly later in 2018 is EastEnders actress Lorna Fitzgerald.
And boxer Frank Bruno is also keen to sign up, quoted as saying this week: “I would love to do Strictly. I’d like to do a bit where I breakdance on my own.”
However Spice Girls' Geri Horner has ruled herself out of Strictly Come Dancing, suggesting it was "too much hard work".
"I’m not a trained dancer so when I was with the girls it always used to take me about four hours longer than everyone else to learn a dance routine," Geri told The Sun newspaper. "It does look like so much fun and I love the show, but too much hard work."
Strictly Come Dancing airs on BBC One.
The line up is usually confirmed in September time.