Maldini and Massara, along with Zvonimir Boban, were the key men in building last season's title winning team.
However, neither director has had his contract renewed.
Galli told La Gazzetta dello Sport: "It is a surprise for everyone that the two renewals, they would have deserved the extension after the championship is over.
"I think it can be resolved shortly, I don't think the owners want to let them slip away.
"A compromise can and must be found, for the sake of everything and everyone will have to put aside a little bit of pride also because it seems to me that at the moment Milan is losing the possibility of moving on the market in a certain way."