Pere Guardiola reportedly spent several hours at the Giannino restaurant in Milan - where Galliani regularly holds business meetings - with Italian newspaper Gazzetta dello Sport among those suggesting discussions took place concerning a possible future role at the San Siro for the unemployed coach.
But the Rossoneri quickly issued a statement on the club's official website denying any contact between the two parties.
It read: "AC Milan denies the occurrence of a presumed meeting between vice president Adriano Galliani with family or agents of Mr Guardiola, following news stories that have emerged from several outlets."
Pep Guardiola has been living in New York since leaving Barcelona at the end of last season, with the 41-year-old Catalan yet to give a strong indication of when, or if, he will return to football management.
Current Milan boss Massimiliano Allegri has endured a difficult start to the Serie A season, losing five of the opening eight games, but Saturday's comprehensive 5-1 victory over Chievo saw the Diavolo return to the top half of the table.
The Rossoneri take on Primera Division side Malaga at the San Siro this evening as both clubs vie for qualification from the Champions League group stages.