The 29-year-old has been in great form for the Serie A side this season.
While the Foxes are planning to offer the 29-year-old a three-year contract at the King Power Stadium - should they see a bid accepted - the Mail hints that they are wary of offering a considerably larger fee due to his age.
However, if Claudio Ranieri is desperate to land the former Empoli man, he could find that he has to improve his bid once again, as the Mail suggests that Inter Milan are also interested in a move for the Italy international.
Eder has been in stunning form for Sampdoria this term, scoring 12 goals in 19 league games. Only Napoli's Gonzalo Higuain has scored on more occasions in Serie A this season.
It is largely down to his form that Vincenzo Montella's side find themselves slightly clear of the division's bottom three. Without his goals, it is safe to say that the Blucerchiati's five point advantage over Carpi - who currently sit just inside the relegation zone - would not exist.
And while Sampdoria may be desperate to hold onto their key man, he may look at Leicester's current position in the Premier League and feel that the opportunity to be involved in a title fight is one that is too irresistible to turn down.