News sources in Portugal claim that the Sporting player is regarded by the Rossoneri as an adequate substite for aging Gennaro Gattuso, who has been linked with football away from San Siro.
However, Sporting's asking price of 30 million euros for Veloso may prove to be a major stumbling block in his transfer to Italy.
According to news daily A BOLA, Milan are ready to put together a player-plus-cash offer for the 22-year-old which would see Argentine Leandro Grimi going the other way.
Grimi spent half season on loan at Sporting, and despite several approaches from the Lions to finalize his swoop to José Alvalade, the two clubs were never able to come to an agreement.
Now, with Veloso's contract on the table, Grimi could become Sporting's third summer signing of the new campaign behind Fábio Rochemback and Hélder Postiga.
It is understood that the Serie A outfit tried to include Kaká's brother, 22-year-old central defender Digão, in the deal to reach Veloso's release clause, a possibility rejected by the Portuguese runners-up.
In case Sporting give AC Milan the green light to negotiate terms with Veloso, Premier League teams Manchester United and Arsenal are expected to make a move for the midfielder, who is currently on international duty with the Portuguese national squad.