Gueye has been a superb servant for the Blues ever since he returned from a spell with another team in the French top flight, PSG, in 2022.
The Senegal star had enjoyed a productive time at Everton when he originally joined from Aston Villa in summer 2016 after the Midlands club were relegated to the Championship.
However, he has been even more instrumental an asset for the Toffees since that return, and indeed he seems to be aging like fine wine with his performances getting better and better the older he is.
This season, he has produced some superb displays, anchoring the midfield and providing a terrific shield for the Everton defence.
Now, though, he, along with a number of other veteran players such as goalkeepers Asmir Begovic and Joao Virginia, midfielder Abdoulaye Doucoure, and centre-back Michael Keane, are out of contract in a few weeks' time.
Begovic, Virginia, and Doucoure are leaving the club, and Keane's future is still uncertain, while attention is also increasingly turning to Gueye and whether he too will depart for pastures new.
Everton manager David Moyes and the club's new executives have a number of big decisions to make this summer and likely face a huge rebuilding job with so many established players leaving the first-team squad.
One player the Blues must do all they can to persuade to sign another deal is Gueye. While a revamped squad should be made up predominantly of younger players as the club move into the new Hill-Dickinson Stadium, a few older heads will still be needed and be very valuable too.
Despite this, those reports surfacing today claim that the 35-year-old Senegal international could very well return to France and another Paris club this summer.
But Gana's ball-winning qualities, leadership, and the huge Premier League experience he offers are surely too good for Everton to let him go without a fight.
And replacing him with a player of comparable ability and experience without breaking the bank would prove a tough challenge.