Muriqi has become a wanted man in Europe after he impressed in his debut season at Fenerbahce, scoring 15 goals and providing six assists from 32 league games.
Serie A club Lazio are keen on adding the Kosovo international to their ranks after earning a spot in next season’s Champions League.
The Biancocelesti are pushing to get a deal done for the 26-year-old striker, with a fee in the region of €18m mooted.
With Muriqi potentially on his way out, Turkish Super Lig club Fenerbahce have identified Everton centre-forward Tosun as a candidate to replace the Kosovan.
However, the Turkey international is claimed to be keen on continuing his career abroad, with two years still left on his contract with Everton.
Fenerbahce are hoping that Tosun has a change of heart.
And the Turkish giants will open talks with Everton if they receive the green light from the striker.
Tosun joined Everton from Fenerbahce’s league rivals Besiktas for a fee in the region of £20m in January 2018.