The 25-year-old's impressive performances in the Primera Liga last season have reportedly turned heads across Europe.
Fulham are thought to have made an unsuccessful bid for his services, while Inter Milan, Juventus and Atletico Madrid are all allegedly interested in the forward.
Osvaldo's agent, Dario Decoud, says Spurs have also joined the race to sign the talented Italian-Argentine.
But he claims the striker could snub a move to White Hart Lane in favour of joining an Italian side.
"Atletico Madrid and Tottenham like him, but it is early to speak of a transfer," Decoud told calciomercato.it.
"It is true that the two clubs (Inter Milan and Juventus) like the player and I can reveal that there have been contacts with them.
"Osvaldo would like to return to Italy and Inter Milan and Juventus are two great teams.
"Now Pablo is on vacation and from July we will know more."
Espanyol are reportedly looking to hold out for the €20million (£17m) buy-out clause inserted in the striker's contract when he sealed a permanent move to the Barcelona club from Bologna last summer.
But Decoud believes a transfer could go through for less, adding: "Espanyol are asking for €20m, but I think the deal can go through for €15-16m."