The TV stars have reportedly been dating in secret for the last year after bonding over their love of keeping fit.
Sykes, 47, has yet to comment on the claims, but Murs, 33, appeared to laugh them off on Twitter.
The singer shared a gif off Anchorman’s Brick Tamland laughing next to the words “good one”.
The pair are said to have been introduced by a mutual friend, before romance blossomed after a string of under-the-radar dates.
A source told The Sun: “Mel loves a younger man and really fell for Olly when he got into shape late last year.
“They were initially introduced through a mutual friend. They started texting for ages and some of the messages ended up getting quite saucy.
“They have both been determined for nobody to find out. It’s been a bit off and on and there’s a real physical attraction between them.”
Sykes has two children, Roman, 15, and Valentino, 12 from her marriage to actor Daniel Caltagirone, which ended in 2008.
She married 29-year-old Jack Cockings in 2013 but filed for divorce less than a year later, describing it as a “difficult” time.
Murs dated Francesca Thomas for three years before calling time on the relationship in 2015.