Toffees boss Frank Lampard is keen for two midfielders to be brought in through the door before the transfer window closes on 1st September.
Gueye, who Paris Saint-Germain are looking to offload soon, is a popular option on Merseyside and Everton are ready to step up their pursuit.
Any move would be likely to be a permanent one, but Gueye’s camp want a two or three-year contract for their client if he does join.
Everton are claimed to prefer the shorter option, a two-year deal, taking into account that Gueye is now 32 years old.
It remains to be seen if Gueye feels that offers him the security he requires as he enters the latter stages of his career.
Everton sold Gueye to PSG in 2019, with the midfielder having been sold on a switch to the Parc des Princes.
He is now out of favour in France and is suggested to be in favour of returning to Goodison Park as he seeks regular game time.
