Everton have been trying to tie the veteran midfielder down to another deal ever since the season ended and have apparently offered him a one-year contract extension.
However, other reports have suggested Gueye wants a longer-term deal, maybe for a further two years, before he will commit to signing with the Toffees again.
Now, according to fresh stories, the 35-year-old Senegal international will decide his next move is to return to French football, where he previously enjoyed a spell at PSG after first leaving Everton.
Losing Gueye would represent a serious blow to the Blues and David Moyes as he faces a huge task anyway, rebuilding a threadbare squad with a number of senior players having either already left the club or possibly about to do so.
Plenty of reports have been coming out with some claiming very substantial sums are being made available to Moyes in order for him to complete this restructuring, but the exact amount is uncertain, and so the number of players that can be signed is still speculative.
A series of midfielders have been linked with a move to the Toffees, whether Gueye does in fact depart in the end, or even if he were to stay.
Replacing Gueye would be a big task as he was the defensive midfielder putting in the most tackles per game in Europe last season, averaging 3.6 a match, according to some analysis.
Presumably, especially looking at how he wants Everton to operate, Moyes would be looking for a player who is a like-for-like replacement for Gueye and so will need a highly energetic, high-tackling number six type of player. They are out there, but not too many might be available.
The Blues have a newly constructed backroom staff brought in to revamp the club's transfer strategy and academy. They will now have to earn their wages, even more so if Gueye does leave the Toffees.