Eyraud has been impressed by on-loan Swans striker Gomis, who has helped Marseille move up to fifth in the Ligue 1 table, and hopes to make the transfer permanent at the end of the season.
Gomis has scored 17 goals in 26 appearances for L'OM this term – four more than he managed in two years at Swansea. The Frenchman signed for the Swans on a free transfer in 2014 after leaving Lyon, but struggled to adapt to the Premier League before returning to France on loan.
Despite the original agreement between the two clubs including no set fee, the Marseille President says a deal is likely to be discussed in the summer.
Speaking to Canal Football Club, Eyraud said: "Gomis is having an exceptional season. We will soon see what happens with him in the coming months."
Swansea continue to fight for Premier League survival, with Paul Clement's men currently three points above the relegation zone, and a deal and agreed fee between the two clubs could depend on whether the Swans can beat the drop.