Jonathan Calleri is currently on loan at Sao Paulo
Calleri, 22, has also been watched by Spurs, Chelsea and Inter Milan.
He is currently on loan to Brazilian outfit Sao Paulo from Uruguayan club Deportivo Maldonado.
Calleri helped former club Boca Juniors win the Primera Division and the Copa Argentina double in 2015 before being acquired by an investor group and loaned to Sao Paulo.
Swansea hope the deal will be made easier due to Calleri qualifying for an Italian passport through his grandparents.
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