The 28-year-old has cemented his position as England's number one since joining the Toffees from Sunderland in 2017 and has made 205 appearances for the Merseyside club.
Pickford has kept 55 clean sheets in that time, and he was awarded Everton's Player of the Year award in the 2017-18 and 2021-22 seasons.
The former Black Cats youngster has fended off competition from Aaron Ramsdale and Nick Pope to hold his place as England's primary shot-stopper, playing every minute at Euro 2020.
Pickford was also lauded for his performances for the Three Lions at the 2018 World Cup, but Everton are at risk of losing the goalkeeper on a free transfer in the summer of 2024.
However, Lampard has confirmed that talks are ongoing over a new deal, telling reporters: "It's something we want to do. We want to get the right solution."
Pickford kept seven clean sheets in the top flight last season to help Everton avoid relegation, and he made eight saves in a Merseyside derby draw with Liverpool earlier this month.
The England international has since picked up a thigh injury and will miss the upcoming international break, with Dean Henderson joining Pope and Ramsdale in his place.
Lampard has reassured Gareth Southgate that Pickford will be fit for the 2022 World Cup, though, adding: "I'll be honest - Jordan would go and play on one quad for England in a friendly next week.
'We have to be sure that we do the right thing. I've spoken to Gareth and our physios and England's physios are in conjunction together, making sure we do the right thing for Jordan.
'And the right thing for Jordan is the right thing for Everton and England. Hopefully it will be in the next two or three weeks and he will be back, it's as simple as that. We wouldn't take any risks with him. If we did, it would affect our batch of games up to the winter break.
"If you were to re-injure the quad, it would obviously affect his run-up to the World Cup. So we are being very careful with that. We are working with Jordan and England. I learnt as a player the negatives of coming back too early.
"I re-injured my quad a few times, trying to push my physio to get me back quicker. I'm now more experienced, so I can be on the other hand and make sure he does it in the right way. The experts are the physios. He's keen but he is very mature. He wants to play but we will find the right way."
Everton are reportedly hopeful that Pickford will be able to return for the clash with Southampton on October 1, as Asmir Begovic prepares to deputise against West Ham United on Sunday.
England have been dealt a further blow with Manchester City midfielder Kalvin Phillips, who is understood to be at risk of missing the World Cup due to a shoulder injury which may require surgery.