Italdesign Giugiaro is owned by Lamborghini, that is owned by Audi, that is owned by VW. So yes, VAG can ask Giugiaro to do whatever they want.
The discussion about VAG (Audi) buying Alfa Romeo make sense, when Walter da Silva worked for Alfa before, Giugiaro designed many Alfa and VAG already owns an italian brand and is successful with it. There is a a large group of ex Alfa employees that work at VAG. They would probably like to work for Alfa with VAG's financial support. Some rumors were that a team at VAG already finalised about 7 projects in the possible case if they buy Alfa. Would like to know what they are like. Could it be the Giugiaro team was working on these projects? Or the Lamborghini team while the delay of the Gallardo replacement chassis?