The 29-year-old spent last season on-loan at West Bromwich Albion, and scored his first goal in English football against Sunderland in a 3-0 win for the Baggies.
The Uruguayan is desperate to bolster his Sunderland side ahead of the new campaign. With no fewer than 12 players leaving at the end of last season, the Black Cats squad is threadbare and in need of some serious strengthening.
The Sunderland manager has already reportedly come to an agreement with Liverpool over the proposed signing of Fabio Borini (subject to personal terms being agreed) and is also reported to be heading into talks with Atletico Madrid in a bid to sign midfielder Cristian Rodriguez.
Amalfitano can operate anywhere across the front of an attacking midfield three, but with Borini and Rodriquez potentially already in the pipeline, it is unsure where the Marseille midfielder would fit into Poyet's plans.
The Sunderland manager's main problem area at this moment in time is in the left-back department.
The Black Cats are currently without a senior left-back on their books, and with negotiations to sign Marcos Alonso seemingly stalling, this has to be considered their priority.
Amalfitano is entering the final year of his contract at Marseille so could be available for a cut-price. But Sunderland will need to act quickly if they are to land the midfielder, with Aston Villa and Crystal Palace also said to be weighing up a move for the 29-year-old.