The QPR attacker, who has had his medical on Thursday, discussed terms with the Rossoneri CEO ahead of his proposed switch to the Giuseppe Meazza for the remainder of the season
The Rossoneri announced on Thursday that the attacker had arrived in Milan to take part in a medical after being given permission by current club QPR to cut short his temporary stay at Fulham in order to link up with Clarence Seedorf's squad for the remainder of the season.
The 24-year-old met with Galliani and other senior club figures for dinner at the 'Giannino' restaurant, with the struggling Serie A side's chief giving a glowing verdict of the Moroccan ahead of his imminent confirmation as a Milan player.
"Taarabt is a very talented player," the Rossoneri CEO told reporters in outside the restaurant. "He manages to dribble past players, and that's exactly the kind of a player that I like.
"I have followed Taarabt for a long time - since he played in the Championship. Taarabt is, of course, very happy and I will see him tonight [Thursday]. We're very satisfied."
The loan move is not expected to be made official early on transfer deadline day despite being all-but-complete, in the same way that Mario Balotelli's permanent switch from Manchester City was confirmed on January 31 last year.
Reports suggest Taarabt - who had been linked with Paris Saint-Germain 18 months ago - can be bought outright by Milan in the summer for €7 million (£5.75m).