The Premier League duo are ready to rival Paris St-Germain for the Senegal worldwide just days after the French champions bid of £21.5m was rejected by the Toffees hierarchy.
However, Everton coach Marco Silva recently said that no new bids have been made for Gueye, who is now nursing a slight injury.
Silva insisted he had not been told of any new offer from PSG for the midfielder and that he had left him out of Tuesday night's 1-0 win at Huddersfield due to a groin injury.
Everton were adamant all through January that Gueye would not be sold - a position that was strengthened by bids they felt were unrealistic - but their stance has upset him; he is 29 and believes the opportunity to move to a club of PSG's stature may be now gone for good.
"I know Idrissa very well, he is a good professional and a fantastic boy", Silva said Friday.
"We tried to be honest with all of you and with our fans". He had a minor problem in his groin.
Since joining Everton he has been one of the Premier League's most consistent midfield performers, and has season been responsible for more than 20 percent of the team's tackles, with 83. No new offers and hopefully he can continue with us.
"When a club like PSG comes in it is normal he starts to think about his future but now he has stopped, the market is closed and I don't have doubts we will see the best Idrissa Gana again". Nobody has told me. Let us know in the comments section below. "Of course after some moments it can become a matter of money, but from my point of view he is a really important player for us", Silva is quoted by the press as saying on Sunday.