Gray, 27, is likely to leave Goodison Park this summer after a two-year association with the Toffees.
The attacker has been an integral part of Everton’s campaign since his arrival at the Merseyside outfit but is now keen on moving to pastures new.
He has agreed personal terms with Marco Silva’s Fulham, with the London club eyeing strengthening their attacking stocks ahead of next season’s campaign.
Everton are prepared to let Gray move on for the right price, but Fulham have not yet met their valuation, despite claims a verbal agreement was in place.
With no fee agreed, Gray’s switch to Craven Cottage is not set in stone and other clubs remain keen to snap him up.
Sean Dyche’s side are working to do business this summer in alignment with the financial constraints they have.
And it remains to be seen how well they will reshape their ranks next season amid their hopes of averting another relegation scrap.