The defender had an impressive loan spell at PSV last season, but he returned to Everton in the summer and is still at Goodison.
The 21-year-old centre-back has emerged as a key player for the Toffees and has started the last four Premier League games.
He has less than two years left on his current deal and Everton are expected to offer him a new contract soon.
But it has been claimed that PSV are plotting a swoop to try and re-sign him in the January transfer window.
The Dutch giants want Branthwaite back in Eindhoven and are prepared to put in an offer to sign him on a permanent deal.
It has been suggested that PSV will table a bid worth €10m in January to test Everton’s resolve.
That figure is unlikely to be enough as the centre-back is now a key part of Sean Dyche’s first-team squad.
Everton are likely to be confident that they will be able to convince the player to continue at the club and sign a new contract.