Long-serving number one Hugo Lloris has now entered the final 18 months of his contract at the Tottenham Hotspur Stadium, and there has been a noticeable decline in his performances this term.
The former France international - who is currently sidelined with a knee injury - is unlikely to be granted an extension, and he will also celebrate his 37th birthday on Boxing Day.
Current number two Fraser Forster is not a long-term option either, while Brandon Austin and Alfie Whiteman only have one senior appearance between them for Tottenham.
As a result, the Lilywhites will be searching far and wide for a new number one for the 2023-24 or 2024-25 seasons, and Pickford has been one of several names linked with a move.
However, Tottenham's hopes of signing the England number one had seemingly been extinguished last month, as Pickford committed his future to Everton with a new contract until 2027.
Nevertheless, The Sun reports that Spurs are still planning to move for the 29-year-old, who is at the top of the goalkeeping transfer shortlist for the upcoming window despite his fresh deal.
Everton and Pickford reportedly agreed to a relegation clause in his new contract, where the former Sunderland shot-stopper will be allowed to leave if the Toffees are demoted to the Championship.
Even if Sean Dyche's side finish in the bottom three, Tottenham would supposedly still have to fork out £35m to sign the England international, but they could try to negotiate a lower fee.
There is not thought to be much difference between Pickford's current wages at Everton and what Tottenham will offer the 29-year-old, who kept his sixth clean sheet of the season in Saturday's 1-0 win over Brentford.
Dwight McNeil's strike after just 35 seconds lifted Everton out of the relegation zone into 15th place, but all five teams below the Toffees have at least one game in hand.
Pickford has recorded 60 clean sheets in 226 appearances for Everton since joining from Sunderland in 2017, and he has been England's number one at their last three major tournaments.
Should Tottenham fail to prise Pickford away from Goodison Park, the Lilywhites could turn their attention to ex-Arsenal and current Aston Villa goalkeeper Emiliano Martinez, whom the Lions are reportedly willing to listen to appropriate offers for.
The World Cup winner would also cost around £35m to bring back to North London, and his exit from Villa could then see Unai Emery's side make an approach for Pickford.
David Raya, Robert Sanchez, Giorgi Mamardashvili and Dean Henderson have also been mentioned as possible replacements for Lloris, who has kept 151 clean sheets in 443 games for Tottenham since joining from Lyon in 2012.