Milivojevic’s game-time reduced significantly this past season under manager Patrick Vieira and he only ended up playing 15 matches in the Premier League.
In contrast, last season had seen him take the pitch 31 times for the Eagles in the league under Roy Hodgson.
Inside Futbol revealed recently that Milivojevic is considering moving on from Crystal Palace as he seeks regular game time next term.
Clubs are keen and now Everton are also interested in the services of the 31 year-old ahead of next season, according to Greek daily Sportime.
Manager Frank Lampard intends to strengthen in midfield for next season and the Toffees could make a move for Milivojevic in the approaching transfer window.
Apart from the Toffees, the midfielder is also of interest to Fulham, and the Greek star has worked with Cottagers boss Marco Silva in the past, and Olympiacos.
Milivojevic has been with the Eagles since the summer of 2017 and in that time has made nearly 180 appearances for the club.
His contract runs out next summer.
