Tranmere host Morecambe in the League Two play-offs on Thursday evening with Ian Dawes in temporary charge following the sacking of Keith Hill earlier this month.
Challinor, who has guided Pools to a play-off finish himself, was priced as a 16/1 outsider with Bet Victor last week but has since moved to become the 4/1 favourite as it stands.
The Pools boss has a history at Tranmere, making 140 league appearances for the club between 1994 and 2002 but has that he wasn't aware of any interest.
“It was absolutely a surprise,” he told The Mail. “It’s speculation and when it comes to speculation, whether it be players or managers, if you’re not getting linked with other clubs then you’re probably not doing a great job.”
Challinor’s Pools side currently sit fourth in the National League table and have the chance at a return to the Football League via the play-offs, a mission he intends on completing.
"Speculation is part and parcel of what the media is about, there’s that much of it and of course it’s good and flattering to be linked but that’s as far as it goes,” he added.
"We know where we’re at and we’re coming into a very exciting part of the season for us with some really big games that we’re looking forward to.
"We’ve got a huge chance and a huge opportunity so it’s one we want to be fully focused on and make sure we take.”