"I would sign him on a permanent basis if I could," smiled Carletto.
"He is not a tourist. His presence can bring extra enthusiasm, as he is an important player and a great professional.
"Even if it is only short-term, his quality can be useful in certain circumstances. He won't have trouble settling in, as football is a universal language and everyone is happy he'll be here. I see no contradiction in that."
The temporary switch will allow Becks to be in the public spotlight ahead of future England games, while Milan are said to be picking up £7m in sponsorship deals for the brief stay at San Siro.
"I would like him to stay. Perhaps we will be of use to him because we are letting him train, or he could be useful for us even for just one game, and that would already be positive.
"In the moment when he is training and in good shape, he'll be in competition for a starting spot along with the others and it'll be up to me to choose."