The 18-year-old is being hailed as one League Two’s top emerging talents, and has developed into a key man for the Chairboys despite his young age.
Toffees chief Roberto Martinez is thought have been alerted by his fledgling displays and is ready to step up his interest in the teenager.
Hause broke into Wycombe’s first-team last year after joining the club from West Ham’s youth set-up.
He is rated highly by Gary Ainsworth, but the fourth tier side are aware that they may eventually have to sell.
Scouts from the likes of Blackpool, West Brom and Huddersfield have all been watching Hause, but it is thought that Everton currently lead the queue for his signature.
The starlet is out of action at the moment with an ankle injury, but with a return to fitness expected ahead of Christmas, he could be the subject of serious January moves.
Martinez is thought to have made a new defender a priority for the coming windows, with Sylvain Distin entering the final stages of his career and Dutchman Johnny Heitinga set to leave Goodison Park.