The former Italy under-21 striker could be on his way back to Serie A as the Stadio Olimpico side have shown an interest in signing him
Roma coach Luis Enrique is eager to add another striker to his squad and had initially set his sights on Nilmar, however, the Stadio Olimpico side are reluctant to meet Villarreal's asking price for the Brazil international and have therefore turned their attention to Osvaldo.
The former Italy under-21 international has a contract until the summer of 2015, but Espanyol are willing to cash in on the forward if an offer in the region of €15 million were to be received.
Osvaldo has previously been linked with Tottenham Hotspur, Atletico Madrid and Sevilla, but Roma, who have already secured the transfer of Bojan Krkic from Barcelona this summer, are hopeful of luring the 25-year-old back to Italy instead.
The Buenos Aires-born forward previously played in the peninsula at Atalanta, Lecce, Fiorentina and Bologna before joining Espanyol in January 2010.