The 30-year-old enjoyed an impressive spell at Besiktas before arriving at Goodison Park in 2018, but the experienced striker has largely struggled to make his mark in the Premier League.
Tosun has scored just 11 goals in 58 appearances for Everton and has recently spent time out on loan with Crystal Palace and Besiktas.
The Turkey international is now back with the Toffees ahead of the 2021-22 campaign, but according to the Liverpool Echo, the striker is not in Benitez's plans for the new season.
Tosun's current deal with the Merseyside giants is due to expire next June, meaning that the club are not in a strong position to negotiate a high fee with potential suitors.
Everton, who will play their final friendly of the summer against Manchester United on August 7, are also believed to be willing to entertain offers for Portuguese midfielder Andre Gomes. body check tags ::