Troilo joined Parma from Racing Club de Belgrano in Argentina last summer for €7 million.
His first few weeks in Italy were difficult — he started just once in the opening ten league games — but he has since developed into a regular starter under head coach Carlos Cuesta and was instrumental in a 1-0 win over AC Milan last month when he scored the only goal. He has started each of the last three league matches.
No formal negotiations have taken place between Brentford and Parma, but the Premier League is described by Tuttomercatoweb as "buzzing" around the 22-year-old.
Brentford are said to need to make a "compelling offer" to have any realistic chance of signing him, given his contract runs until 2030 and his value has risen significantly since his arrival.
Parma have already identified Nosa Obaretin as a potential replacement, suggesting the club is prepared for the possibility of losing Troilo if a club meets their valuation.
His age, contract length and recent form make a fee in the region of €15-20 million a realistic expectation.