It is understood representatives of the Spanish side have made contact with Sami's new agent, Carmine "Mino" Raiola, to enquire about the Greek international, who has spent five years at the club.
The 28-year-old is out of contract at the end of this season and is believed to have impressed Sevilla with his outstanding form against Barcelona in the recent Group H meeting with the Catalans.
Hoops chief executive Peter Lawwell has admitted he is due to sit down for contract talks with the player's representatives next week as he looks to thrash out a similar deal to the three-year extension agreed with fellow-frontman Anthony Stokes.
Samaras scored his 50th league goal for the club in last Sunday's 2-1 win over Partick Thistle and Lawwell has made it a priority to nail down the big striker before the turn of the year.
Although Sami's contract is up at the end of the season, the Hoops remain favourites to keep the player at Parkhead.