Dyche has remained tight-lipped at press conferences ever since the Everton job became vacant, with the Burnley boss keen to avoid the spotlight.
However, the Telegraph claim that Dyche is far more interested in Everton than he has let on.
The problem for the 46-year-old boss is that Everton do not appear to have placed him high up on their wishlist.
Dyche was the early front runner to take over from Ronald Koeman, but as the weeks have gone by, the links have died down.
Everton have considered appointing Sam Allardyce and Marco Silva, but have found bringing either of the pair to Merseyside to be problematic.
Dyche, meanwhile, has continued to impress at Burnley - with his side currently sitting in seventh place in the Premier League table.
Everton have most recently been linked with Martin O’Neill, but Dyche could still be a possibility, if the Republic of Ireland boss’s potential move falls through.