The Rossoneri have made no secret of their admiration for the Argentina striker, who is currently back in South America after a dispute with Manchester City which centres around his conduct during the Champions League loss at Bayern Munich in September.
Paris St Germain have also been linked but Milan owner Berlusconi has urged the 27-year-old to put footballing reasons at the top of his agenda as he seeks a new club.
"If he comes with us, he will win the Golden Ball award," Berlusconi told the Gazzetta dello Sport newspaper. "Tevez has two options, one which regards prestige and the other one money.
"Milan is prestige and he would have the possibility to showcase his talent around the world and win the Golden Ball with us.
"PSG represents a strong economic force.
"He must choose between one or the other."
Milan vice-president Adriano Galliani announced on Wednesday the Rossoneri would not enter a bidding war with PSG for Tevez.
The Italian champions, looking to fill a striking vacancy created by Antonio Cassano's heart problem, have made an offer to take Tevez on loan in January with an option to make his stay at the San Siro permanent next summer but City are not thought to be keen on an initial temporary deal.
Meanwhile, Berlusconi, who resigned as Italian prime minister last month, remains confident coach Massimiliano Allegri will soon sign a contract extension.
Allegri's current deal expires at the end of this season but he has been offered fresh terms which would tie him to the club until June 2014.
"Allegri's renewal is not in dispute," Berlusconi added.
"It's an extension that we had already agreed for some time. He is doing very well."
The former Cagliari coach led Milan to the Serie A title last season in his first year in charge and the Rossoneri are currently third, two points behind leaders Juventus.