The 28-year-old forward has been the centre of much transfer interest in the last few weeks, and it looks as if Palace have made the first concrete approaches to sign the Italian international, with TMW claiming an offer has been made.
Eder, who netted 12 goals and registered five assists in 31 games last season, has been linked with a move to West Ham, Stoke City and Palace previously by the Daily Star, whilst it was reported by the same media outlet that Southampton are considering a move for him.
However, Palace, who are planning on overseeing a major squad rebuild this summer with Alan Pardew enjoying his first pre-season as manager, have already made Sampdoria an offer for his services.
Yet, the TMW report states that the €10 million bid submitted by the Eagles was not enough to tempt Sampdoria, and they intend to keep him in Genoa unless a better offer is made.
Being a winger, who can also play through the centre as a number 10 or out-and-out striker, Eder would look to be a great signing for Palace.
Pardew has shown a desire to improve his attacking force, with the likes of Dwight Gayle and Glenn Murray expected to leave Selhurst Park, and signing a full Italian international as their replacement would be a real sign of intent from Palace as they look to start fighting for European qualification.