According to Gianluca Di Marzio, the Toffees are keen on both Robin Olsen and Sergio Romero, with discussions taking place for the Roma and Manchester United glovesmen.
Olsen, 30, is expected to leave Roma before the 11pm transfer deadline having spent last season on loan with their Serie A rivals Cagliari, while Man United are prepared to cash in on Romero as he fell to third choice in the pecking order earlier this year when Dean Henderson returned to Old Trafford from his loan spell at Sheffield United.
Ole Gunnar Solskjaer has preferred David de Gea as his No.1 with Henderson as back-up, with Lee Grant also on Manchester United's books as a homegrown third option.
LATEST FOOTBALL NEWS
deadline
Man United confirm Telles and want more, Partey flying to England, Walcott medical
confirmed
Man United complete signing of player Roberto Carlos called 'phenomenon'
Goss
Arsenal transfer news live: Partey move made, late Lemar interest, Saliba to Fulham?
goss
Man United transfer news live: Telles signs, Sarr offer, Traore to join
sorry
England trio kept away from squad amid FA investigation, Sancho and Abraham apologise
gone
Arsenal midfielder secures Emirates exit as Bundesliga loan confirmed
swoop
Southampton to re-sign Walcott - 15 years after he left club for Arsenal
profile
'Amazing' Partey could have played for Man United, but is set to fill Arsenal void
SUMMER SPREE
Aston Villa have had the best transfer window of any club, talkSPORT told
last gasp
Partey having medical as Arsenal make £45m move and Guendouzi exits
Both keepers are now being eyed by high-flying Everton, with manager Carlo Ancelotti keen on adding a new gloveman before the transfer window slams shut.
Despite the Toffees' perfect start to the season which sees them top of the Premier League with a 100 per cent record, questions are still being asked of Pickford in goal.
Despite being a talented shot-stopper Pickford remains one of the most mistake-ridden keepers around and he made another error last Saturday as Everton beat Brighton, dropping the ball at the feet of Neal Maupay who willingly converted from close range.
Pickford has now made the joint-most errors leading to goals since the start of last season, making five mistakes along with Newcastle's Martin Dubravka.
That's more than Chelsea's Kepa Arrizabalaga, who has come under serious scrutiny for his mistakes in recent months despite making just two errors leading to goals.
Everton are in talks to sign a new goalkeeper after Jordan Pickford's latest mistake.