The report explains how the Toffees see Hughes a potential replacement for under-fire boss Roberto Martinez, yet Stoke have their own plans of moving the club forward.
Now, amid new TV deals and deeper pockets financially, Stoke have smashed their club transfer record with a £18.2 million deal for Giannelli Imbula and brought in former Champions League winners.
The club is very much established in the top-flight, and the aim is to now go on and qualify for Europe.
Everton, backed by new major investor Farhad Moshiri, have the funds available to challenge for the top four and the club are backed up by a proud history and a huge number of supporters.
However, the Mirror report how the Stoke board are confident Hughes would not trade the Britannia Stadium for Goodison Park, owing to the club’s promise to spend big in their bid for Europe and continue growing.
The two clubs are currently separated by six points in the Premier League, with Stoke occupying 10th spot and Martinez’s under-performing Everton side one place below with a game in hand.