Balotelli joined Marseille from Nice in January on a short-term contract and enjoyed a solid end to the season, scoring eight goals in 15 Ligue 1 appearances.
Marseille had been keen on keeping him at the club, but their failure to qualify for the UEFA Champions League has forced it to lower its wage budget.
Lucas Ocampos has already left for Sevilla, while Kevin Strootman, Adil Rami, Luiz Gustavo and their highest-earning players are being linked with moves.
Balotelli's exit has now been confirmed, opening the door for the striker to return to either Italy or England, having been linked with Napoli and West Ham.
"At the moment we are [working] on two or three areas to adapt if there are unexpected departures and that we would have to replace," Eyraud told L'Equipe.
"The attacking position has to be filled, since Mario Balotelli will not continue with Marseille. We are looking beyond the position of attacker, however, including centre-back."
Eyraud is hopeful highly rated 19-year-old centre-back Boubacar Kamara signs a new deal, while he also denied reports Marseille have told Rami – a World Cup winner with France last year – to look for a new club.
"I respect my players, I rub shoulders with them every day and I see how much pressure they are under," he added. "I am very surprised by the media coverage that claims Rami has already left.
"What is certain, for me, is that Adil Rami must question himself, deeply, about his status, about his job as a professional footballer, about his rights and duties as a player, and moreover a world champion.
"With Adil I am very frank, very direct, as always, and I will make a decision at the end of this discussion.
"I cannot wait to have it [the discussion with Rami], and to have this exchange with him, which will take place this week."