The winger played a key role in helping Everton avoid relegation from the Premier League last term, chipping in with key goals.
Gray however wants to move on this summer and a host of sides have been chasing his services.
Fulham look to have now won the hunt for Gray as they have a verbal agreement in place with Everton and personal terms will not be an issue.
However, Everton will not sign off on Gray’s exit from Goodison until they have brought in further bodies for Dyche.
Dyche is aiming to strengthen his attacking options and is working on a swoop for Sporting Lisbon teenager Youssef Chermiti.
Losing Gray will be a blow for Everton, but it is one they are willing to absorb if he can be replaced.
Everton have already snapped up Ashley Young as a free agent and landed Arnaut Danjuma on loan this summer.
