At 24 years of age, a player who made history in Russia over the summer by becoming the youngest man to keep a clean sheet for the Three Lions on the grandest of sporting stages has seen his profile enhanced considerably.
He is already the most expensive British goalkeeper of all time, with Everton having snapped him up for £25 million ($33m) in the summer of 2017, but another big-money move could be on the cards at some stage.
Moyes, who made Pickford first choice at Sunderland during his time in charge at the Stadium of Light, hopes no switch will be made this year, with it important for an emerging talent to continue furthering his development in settled Premier League surroundings.
“It’s a big club, he’s only just moved and I would say to him it would be stupid to even consider another move if there was to be an option for him.
“I think it will help him being at Everton because he will get enough work and he’s got a chance to develop without every single thing he does being scrutinised.
“He is still young and he just needs to keep getting his games in. The last thing he needs to bother about is any speculation.
“If you go to the World Cup and do as well as he has done, you’ve shown you can stand on any stage.
“But all he needs to do is go back to Everton, keep working and look to improve. Don’t let anything slip, don’t be complacent.
“At the moment he is a young player who has played very well. But the key to being a top player is going back and performing just as well.”
Moyes has also backed Pickford to nail down the No. 1 jersey with England, with it possible that he could occupy that shirt for the next decade.
He added: “Near enough everybody accepts him as England’s No. 1 now and, at the age he is, that shows how good he is.
“But there’s also a chance that if he does it right, there is longevity for him. He could easily be England’s No. 1 for the next 10 years.
"He was always going to reach the top level because he’s got the ability.
“It was always about him putting the hours in, making sure he eats well and lives well.
“He looks much leaner now and he’s got himself in really good physical condition. But now it is up to him to maintain and improve on his standards.
“So many of the players now have their own chef and that might be one of the things Jordan could do if he’s looking to gain that one per cent extra.”