The 25-year-old scored 13 goals for the Estadi Cornellà-El Prat outfit last season, as Espanyol defied their tag of perennial strugglers to finish in eighth place, narrowly missing out on a qualification spot for the Europa League.
As a result, a host of European outfits are believed to be tracking the Argentine goal-getter, who joined Espanyol from Bologna, having spent four years in Italy with the Rossoblù, Lecce and Fiorentina.
Tottenham Hotspur, Juventus, Inter Milan and Atletico Madrid are all thought to be keen on recruiting the former Huracan front-man.
However, Osvaldo has stated that he is not looking for a move away from Espanyol, and would like to captain the side.
"I want to stay and I would love to be captain," Oslavdo told Efe. "I think only about Espanyol. It shows in my mood and in training, I am happy here.
"My agent does his job, but I just focus on playing and I have a contract in place. My agent is like a father to me, he is very concerned about my future.
"I would love to captain Espanyol, but this is something that needs to be decided on between all partners.
"I feel very identified with this team and with the project, so I want to stay here."
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