Baroni, 17, made his senior debut for the Argentine club last year and has since become a regular fixture in their first team.
The attacking midfielder has scored one goal and provided three assists in 14 first-team appearances across all competitions so far.
Baroni comes from a footballing family at Talleres, with his father Gonzalo and grandfather Leonardo both having played for the Cordoba club, while his older brother Thiago is currently in the reserve team.
A left-footed playmaker who operates in the classic Argentine enganche role, Baroni made his senior bow against Newell's Old Boys in January and set up a goal on his debut.
Di Marzio's report states that Baroni's contract contains a release clause worth €25m.
Talleres could, however, be willing to sell the player for around €15m plus add-ons, according to the same report.
Baroni's contract with the Argentine club runs until 2028, having recently signed an extension that reflects his rising value.
His performances for the first team have come under the watch of head coach Carlos Tevez, who handed Baroni his senior debut and has since become an outspoken admirer of his ability.
The teenager was also named the best under-17 player in Argentina following a standout campaign at international youth level this year, a factor that has only sharpened the interest from Europe's leading clubs.
Baroni's Italian heritage means he is also set to qualify for an Italian passport in the near future, a detail that has made a move to Serie A more straightforward to arrange than for some of his rivals' suitors.
With Borussia Dortmund, Chelsea and Fiorentina - three major clubs from three different leagues - now circling, Talleres face the prospect of losing one of their most promising academy products before he has even turned 18.