The Goodison Park outfit are currently without a manager after Carlo Ancelotti opted to leave to take charge at Real Madrid.
However, with a director of football in place in the shape of Marcel Brands, Everton are still putting into place plans in the transfer window.
And Brands is keen on countryman Dumfries, according to Dutch daily the Eindhovens Dagblad, a player he knows well from his time at PSV Eindhoven and is a firm admirer of.
It is claimed that PSV Eindhoven are prepared to let Dumfries go for the right price and will value the defender at around €15m.
Dumfries still has another two years left on his contract in Eindhoven, but is open to a move away from the club.
Everton are not the only top club keen on the defender, who also has other admirers.
The full-back has been capped by Netherlands at international level and has been included in the country’s squad for Euro 2020.
