The Premier League club indicated to Roma they were willing to pay a club-record fee to entice the Italy international to St Mary’s Stadium.
But Osvaldo has snubbed the interest from the Saints as he holds out for a move to a higher profile club.
It is understood that Southampton were willing to pay up to £17m including add-ons for the Argentine-born forward, who joined Roma from Espanyol in 2011 in a deal worth up to £14.75m.
The Serie A club are willing to offload the 27-year-old this summer in an attempt to provide funds for new manager Rudy Garcia to re-shape his squad.
Tottenham met with Osvaldo’s representatives earlier this year and the player himself was keen to move to White Hart Lane but the Londoners have now dropped their interest as they close in on the signing of David Villa from Barcelona.
It is understood that former Roma general manager Franco Baldini, who took up a new role as Spurs’ technical director this month, has doubts about the controversial Osvaldo’s attitude.
Atletico Madrid have also enquired about signing Osvaldo but they have now opened talks with Sevilla about Alvaro Negredo, who is set to be sold by the cash-strapped Spanish club.
Osvaldo’s salary expectations are not an insurmountable problem for Premier League clubs flush with money from the new broadcasting deal.
The striker currently earns £61,000-a-week at Roma, a sum that will rise to £72,500-a-week in the final year of his contract, which runs until 2016.