Alvarez is in limbo due to disputes between Sunderland and Internazionale.
Alvarez spent last season on loan at Sunderland from the Serie A club, and in his contract they were forced to purchase him outright if he played a certain number of games.
However, they refused to see through the deal, believing that Inter had acted incorrectly when it came to sanctioning surgery on an injury Alvarez had.
This meant that Sunderland did not want to sign him, but Inter did not want to take him back, meaning Alvarez, 27, was without a club despite being legally owned by two.
A dispute between the two clubs has seen the winger remain on the outskirts, and he has yet to appear this season whilst FIFA deal with the case.
With neither club wanting him, it is up to Alvarez to find a new club, and the report claims he has started training with Velez Sarsfield of Argentina - the club at which he started his career.
He will be hoping to earn a permanent contract with the club, although due to his contract status, he is not officially allowed to sign with a new team until the January transfer window.
It is expected that Alvarez will leave both Sunderland and Inter permanently when 2016 rolls around, with Velez the most likely club to secure his signature.