The 34-year-old initially spent three years with the Toffees between 2016 and 2019 and made 108 appearances before joining Paris Saint-Germain for around £30m.
Gueye then returned to Everton for a reported £2m in August 2022 and has since featured 57 times in all competitions, including 23 outings so far this season.
The Senegal international has played regularly under manager Sean Dyche this term, but a groin injury has reduced his minutes in recent weeks.
Gueye is due to see his current contract at Goodison Park expire at the end of the season and there are currently no signs to suggest that he will be offered a new deal.
Gueye keen to make Middle East move
According to Football Insider, Everton have the option to extend Gueye's contract by an additional 12 months, but they Merseysiders are not looking to trigger the necessary clause, even if they avoid relegation from the Premier League.
The report adds that Everton are keen to remove the midfielder's £80,000-a-week wages off their books in order to improve their financial situation.
It is claimed that Saudi Pro League clubs are 'ready to approach' Gueye this summer and the Senegalese would be interested in moving to the Middle East when his Toffees contract expires.
Joining a Saudi Arabian club is said to be viewed as 'an attractive proposition' for Gueye, who will turn 35 in September.
Who else could leave Everton this summer?
Everton's financial predicament and uncertainty over their Premier League status has led to speculation over the future of a number of first-team players ahead of the summer transfer window.
The Toffees have been charged twice this season for breaching the Premier League's Profit and Sustainability Rules and have subsequently been deducted a total of eight points, leaving them 16th in the table and just two points above the relegation zone.
Should Everton fail to avoid the drop this season, star players including Jarrad Branthwaite and Amadou Onana, who have recently been linked with Manchester United, could be sold for substantial fees in the summer.
Meanwhile, Gueye is one of six Everton players, along with captain Seamus Coleman, Andre Gomes, Ashley Young, Dele Alli and Andy Lonergan, who is out of contract in June and faces an uncertain future at Goodison Park, as does Arnaut Danjuma who is on loan from Villarreal.