With the La Liga giants unable to register any new players until 2018 due to a FIFA-imposed transfer ban, however, Costa faces the prospect of being in a footballing limbo.
Eyraud has therefore decided to step in, telling SFR Sport: "What I like about the player is his character, his passion and his willingness to fight. He would fit in well with our team.
"I understand he was a complicated contractual situation at Chelsea. But if it a player ticks all the boxes, we could reach a bid of up to £27.5m.
"We know how to move cleverly in the transfer market — but certain conditions need to be met. For this reason, nothing is impossible."
Costa, currently on strike in Brazil, is said to have been warned that he must return to training with Chelsea or risk being heavily fined.