The midfielder played an influential role in Everton’s season which saw their midfield torn apart by injuries.
However, according to The Times, there is currently a major sticking point in the contract negotiations between the two parties.
Everton are said to have offered Gueye a new one-year deal to remain on Merseyside, but the midfielder is looking for a two-year offer.
Gueye really impressed for Senegal against England earlier this week as he carried on his fine form from the season.
The 35-year-old may not have age on his side, but he is not allowing that to prevent him from playing some of his best football in an Everton shirt.
If Everton do not provide him with what he wants, it seems like another club will be more than happy to do so.
But the report from Joyce has claimed he and Michael Keane are set to depart at the end of the month.
In recent days, Newcastle United pulled out of the running for Calvert-Lewin, which will be a blow for a player who wants to play Champions League football.
As for Keane, Everton are wanting to add a new defender and his departure is one which was probably expected.
Losing Gueye will be a real blow and will certainly take some replacing in the market which would only add to the huge amount of work needing to be done.
