Tosun is said to be a long-term target for Palace and the Turkey forward is reportedly desperate for regular football ahead of Euro 2020 this summer.
According to the Liverpool Echo, a short-term switch to Selhurst Park is moving closer after Ancelotti met with director of football Marcel Brands to discuss the deal this week.
The report adds that Everton value Tosun at £20m and hope to move him on permanently in the summer.
Tosun joined Everton from Besiktas in January 2018 and has scored 10 goals in 47 appearances for the Toffees.
However, he has fallen out of favour under Ancelotti and was used sparingly earlier in the season too, making just four appearances in total.