The attacking midfielder, who missed a penalty in Belgium's 1-1 draw with Turkey on Friday, could be on his way to San Siro to boost the Italian champions' midfield
Galliani's admission follows on from reports that Standard's vice-president Luciano D'Onofrio had travelled to Italy to discuss a transfer.
"We are talking with Standard Liege," Galliani told Sky Sport 24.
There was also confirmation from D'Onofrio, who travelled to Milan earlier in the week.
"I spoke with the Milan hierarchy,” he revealed. “We had a chat for a few hours yesterday."
Witsel has become an integral player for both club and country this season, forging an excellent midfield partnership with Steven Defour.
However, the player recently acknowledged that he needs a move abroad in order to take his game to the next level and explained: "I need to make a move abroad in order to improve. You can see in training with [Vincent] Kompany and [Daniel] van Buyten. They are sharper in the duels and they always behave like a professional," he told Sporza.
"My future? I am happy that I can go on holiday. Do I know something about Milan? No and even if that was the case, I would not say so."
Witsel played in Belgium's crunch Euro 2012 qualifier against Turkey, which the Red Devils drew 1-1. Milan sporting director Ariedo Braida was there to check out Witsel, who missed a 75th minute penalty.