Everton are currently in talks with Jordan Pickford about a new contract.
Pickford has two years remaining on his current Everton deal, but Frank Lampard believes that the goalkeeper could agree to extend his contract next month.
Speaking to reporters ahead of Saturday's league meeting with Nottingham Forest, Lampard said: "The club are speaking with Jordan. He is a massive player for us, everyone wants him to stay and Jordan is very happy here.
"Maybe it is one for the craziness of the window to shut in a couple of weeks and in the cold, calm light of day we can get it done very quickly.
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Lampard was asked about whether Anthony Gordon's situation - with the forward linked with a move to Chelsea - is similar to his own transfer from West Ham to the Blues in 2001.
"I had four years in the first team at West Ham. I got in at 17 and left at 21-22. So it is not a direct comparison.
"I'm not silly, I know players can be ambitious, Chelsea is a club that is always going to be in my bones because of what it did for my career, and what I feel about the fans and what I got out of it, so I have got huge respect and appreciation for that.
"But while I work for Everton and I feel the passion of this club and what this club has done for individuals and what individuals can do for this club then it is my job to hold that closest than anything at the moment.
"So when I have those conversations I think what is best for Everton, what is best for me and my job."
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Commenting on his own time as Chelsea boss when he promoted youth, the 44-year-old stated: "At Chelsea, I brought loads of young players into the team and now they want to take one of my young players.
"Maybe there is an irony in it. But I think it is understandable that people may be interested in players like that, that's the way the world works."
The Everton manager was also questioned by reporters as to whether their reluctance to sell Gordon would affect their chances of signing a Chelsea player on loan.
"I think they are separate conversations, I know the Chelsea players very well. I've got one loan left to use for the UK and it is not just Chelsea we are looking in the area for."
Lampard's side will look to claim their first points of the Premier League season when they play host to Forest on Saturday.
