Holland international Elia, who joined Bremen from Juventus in the summer of 2012, has been established as a Southampton target this winter but Koeman has indicated that it will initially be a temporary agreement between all parties involved.
"He is one of the players on our list to bring in in January - it's still not done but yes, I am interested in the player," Koeman said.
"If he signs for Southampton, I think he will be a good option.
"We need at least one more player up front because we lose Sadio Mane in January for the Africa Cup. We need another player for that position and he is a good option.
"If he does sign for us, it will first be as a loan deal."
Of the 28-time Dutch international, who has also played with ADO Den Haag, FC Twente and Hamburg, Koeman added: "He was a Dutch international, he had not such a good period in Germany but I believe in the qualities of the player.
"He is a wing player and we normally play with both a right winger and a left winger.
"We also like in our style of playing fast people who can play one against one with quality."
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