Brighi has been linked with a move to the San Siro as a replacement for Gennaro Gattuso, who will be out for six months with an injury.
“I have had no contact with Milan, but that is normal because they are a club who behave correctly,” Brighi’s representative Vanni Puzzolo told Radio Radio.
“If the Rossoneri wanted to sign Matteo in January they would contact Roma first before they spoke to us.
“I think it’s just transfer speculation. Brighi is already playing for a great team and Roma are in the Champions League, unlike Milan.
“Doubling Matteo’s wage at the moment isn’t a consideration because he has just signed a renewal and has become a starter at Roma.”