Lucas Biglia has collected 37 international caps for Argentina
The Argentinian midfielder has two years left to run on his current deal but the Serie A giants want to tie him down before this summer's Copa America tournament.
United are set for a summer squad overhaul and Louis van Gaal is keen to add to his midfield options following a second disappointing Premier League campaign, which has seen them miss out on Champions League football next season.
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Football Italia reports Inter Milan and Juventus are also interested in Biglia, who moved to Italy from Belgian side Anderlecht in 2013.
The 30-year-old playmaker has made 27 Serie A appearances this season, scoring four goals and providing three assists.