The Daily Mail says Van Persie's return is timely given the double leg break suffered by Eduardo, although the Dutch striker is likely only to make the bench at the San Siro.
"We will not rush Robin van Persie back but the news is quite good," boss Arsene Wenger told arsenal.com. "It is very difficult to say [when he will be back in the side]. We go step by step. But he should come back into normal training, very, very quickly now.
"Maybe I am being a little over-cautious in my statements but I do not want to put any special pressure on him.
"But the fact that Eduardo is out is one more reason to [get him back]. Also he deserves that championship as well and that is another reason - to do it for him."