The Toffees ended Roberto Martinez’s three-year reign on Thursday after a hugely disappointing season at Goodison Park.
Frank de Boer and Ronald Koeman have been installed as the favourites to succeed the Spaniard but Gray believes the Merseysiders should target their former striker Hughes.
Hughes has done an impressive job in charge of Stoke, rebuilding his reputation after a nightmare spell at QPR, and the 52-year-old has extensive Premier League experience.
Speaking on the Alan Brazil Sports Breakfast, former Everton striker Gray said: “I hope I am not going to upset Stoke fans but when I look at what Mark Hughes has done at Stoke, what he did at Manchester City… he has managed at the highest level, he has got great experience of the Premier League, he knows what Everton is about because he played there.
“If somebody came up to me tomorrow and said they are going after Mark Hughes and his staff, I would be delighted.
“Sparky is at a great age now, he has got all the experience he needs at this level, he knows what the club is all about because he has been there and he understands what you need to be an Everton coach.”
Hughes is contracted to Stoke until 2019 and the Potters would not lose their boss without a fight.
But Gray believes he would quit the club for Everton if the Toffees did come calling.
“I think he would go,” added the Scot. “They are a bigger club [than Stoke].
“You have got new money there, a new major shareholder who is going to pump millions and millions of pounds into the club and it is an amazing place to play your football and to manage.
“I think if they went to Mark Hughes and said ‘we want you’ he would be very, very hard pressed to say no.
“It is a no-brainer, it is a brilliantly safe appointment. I think Sparky would bring a desire and an intensity and the way Everton want to win football matches, he could bring that back to Everton.”