Dyche is the current bookies favourite to replace Ronald Koeman, who was sacked on Monday after just 16 months in charge.
The 46-year-old’s stock is on the rise after guiding Burnley to two promotions and keeping them in the division last season.
The Clarets have also made a fine start to the current campaign, with the club currently in eighth place.
Speaking to the Daily Mail at Monday night’s FIFA awards ceremony in London, Dyche said:
“It's very flattering, I've been linked with other situations before.
“I just keep getting on with my job until things change. It's out of my hands, I'm just getting on with what I do.”
It’s the sort of response you would expect given the circumstances, but by refusing to rule himself out Dyche will only fuel further speculation.
Leicester are also reportedly interested in Dyche, with Sky Sports reporting that the Foxes are stepping up their search for a new boss in the wake of Koeman’s sacking.