Pickford has been linked with a move to Chelsea in recent days after a fine World Cup with England.
The Blues are in the market for a new keeper, with No 1 Thibaut Courtois heavily linked with Real Madrid.
Liverpool legend Jamie Carragher was on talkSPORT this morning talking about Everton with Toffees supporter and former WBC Cruiserweight champion Tony Bellew.
And Carragher could not end the chat without winding up Bellew.
“Yes you’ve got Jordan Pickford, but he’s going to Chelsea isn’t he for £70million,” Carragher jested.
Bellew replied: “He’s going nowhere lad, you leave him alone.”
Carragher says Everton fans should be worried for the upcoming season, claiming they are still two centre-backs short of having a competitive squad.
“They are one of the top clubs in the country, they should always be challenging for European places and they look miles away at the moment,” he added.
“It’s worrying, really worrying.
“We were talking about Liverpool maybe needing a centre-back, I think Everton need two.
“It’s not easy going out there and getting centre-backs at the moment.
“I look at the centre-backs and I really worry.”
Pickford played every single minute for Everton last season in the Premier League.
Meanwhile, another Everton keeper Maarten Stekelenburg has signed a new two-year contract at the club today.