The polarising striker could be heading to MLS this summer if reports out of Argentina are to be believed.
Osvaldo, 29, joined Southampton from Roma in August 2013 for £12.8 million but scored just three goals in 13 appearances before falling out of favour for his part in a touch-line brawl at Newcastle United and a training ground bust up with teammate Jose Fonte.
His off-the-field antics have since forced the Saints to loan him out on three separate occasions to Juventus, Inter Milan and now Boca Juniors, where the Argentine-born forward has managed to keep out of trouble for the most part.
After scoring six times through his first 13 games, Boca would be keen to sign him to a permanent deal but, with the Buenos Aires-based outfit lacking the financial clout, the three-time capped Italian instead looks set to depart when his loan expires on June 30.
With Southampton reluctant to welcome him back, the polarising front man is now expected to be on the hunt for another club this summer, and the Red Bulls could well be his next destination.
The MLS side are in need of another proven goalscorer to take the pressure off 2014 Golden Boot winner Bradley Wright-Phillips, having so far failed to find a suitable replacement for former skipper and star man Thierry Henry, and Osvaldo is said to be one option in consideration.
If head coach Jesse Marsch could manage to get him focused on matters on the pitch then the former Fiorentina man would no doubt prove an inspired signing, but there is no hiding the fact that there would also be a huge amount of risk attached to the rumoured deal.