Scocco, known as "Nacho", arrived on Wearside in January as Poyet invested £3.2million in his services in the search for goals to keep the Black Cats in the Barclays Premier League.
Ultimately, it was a gamble which did not pay off as the 29-year-old Argentinian made only eight appearances and failed to find the back of the net.
Former club Newell's Old Boys have been on his trail for several weeks and River Plate have also expressed an interest as South America beckons once again.
Poyet told the Sunderland Echo: "My first idea - and I knew it would be difficult - was to use Nacho last season to help us get out of the problems we were in.
"It was always going to be difficult for a player who had played in Argentina and Brazil over the last year to come to the English Premier League
"We were in a fight and he's not that type of player - he needed us to be controlling games in order for him to do his bit.
"The type of player he is, we were not playing to his strengths - he needs to be in a team that is on top in games, so my idea then was to take the closed season to improve the team and to improve Nacho in terms of him being used to the environment over here and the football itself.
"But there are options now and everything is being analysed, we will see what happens over the next few days."
Meanwhile, Sunderland's pursuit of Fiorentina full-back Marcos Alonso has been dealt a blow amid reports from Italy that he has been taken off the market.
The Black Cats have been in talks with the Viola over the man who spent the second half of last season on loan at the Stadium of Light for several weeks, and are understood to have made a cash-plus-player offer with Modibo Diakite the make-weight.
But Alonso is reported to have impressed manager Vincenzo Montella in pre-season training and may now have a role to play at Stadio Artemio Franchi.
It remains to be seen whether or not the latest development is a bargaining ploy designed to prompt an improved offer from the Wearside club.
Source : PA
Source: PA