Former Sunderland left-back Michael Gray
Pickford established himself as Sunderland's number one at the start of the campaign, and received his first England call up shortly after.
However, the lifelong Mackems' fan is expected to quit the Stadium of Light in the aftermath of the club's relegation from the Premier League, with as many as eight top flight sides credited with an interest in his services.
Gray, who won two promotions with Sunderland in the 1990s, believes Everton would be a "great move" for Pickford.
However, the 42-year-old is adamant the Wearside club should not let him go for anything less than £20 million.
"It pains me to say it but Jordan is a Premier League goalkeeper," Gray told Talksport on Tuesday. "I was there at the weekend and he pulled off three saves that I couldn't believe. He was phenomenal. His distribution with the ball off the ground is the best I've seen. The bigger guns, they're going to come knocking at the door.
Sunderland goalkeeper Jordan Pickford
"There's speculation about Everton. You look at Everton's goalkeepers - does he improve Everton's starting 11? Absolutely. And I'm sure there'll be two or three others knocking on the door. But what price do you put on a goalkeeper of Jordan's stature? Is it £20 million? Is it £30 million? Anything less than £20 million I think we've been done in - that's how good I think he is.
"I want to keep him at Sunderland but this guy deserves his opportunity to stay in the Premier League and we're not there any more. [Everton's manager, Ronald] Koeman's been at Southampton and he's been at Everton. He's given young players an opportunity and they've thrived on it, and I think he'd fit into Everton's side absolutely no question about it.
"It would [pain] me to see him leave, but I think it'd be a great move for him."
Everton are expected to add to their goalkeeping ranks this summer, with both Joel Robles and Maarten Stekelenburg failing to impress on a consistent basis.
Everton goalkeeper Maarten Stekelenburg
And the Toffees are not thought to be short of cash, following last year's takeover by British-Iranian billionaire Farhad Moshiri.
How much should Everton pay Sunderland for Pickford?
Have something to tell us about this article?