The 27-year-old is negotiating a possible £15.4 million transfer to Vicente Calderon, according to his agent
The Azzurri international, who scored 16 goals in 29 Serie A matches last season, has been linked with the likes of Fiorentina and Tottenham in recent weeks, but a switch to La Liga is now the more likely for the 27-year-old.
“The negotiations are taking place and the fee will be around €18m,” Diego Tavano told Radio Mana Mana Sport.
“The attacker is well liked in Spain and he just needs to find the right emotional balance because he has incredible qualities.”
Atletico are looking for a striker to replace Radamel Falcao who departed for Monaco earlier this month in a €60m (£51.3m) deal.
Osvaldo previously played in La Liga for Espanyol, whom he left to join Roma in 2011 for a fee of €15m (£12.8m).