Aquilani joined moved to San Siro from Anfield on a one-year loan deal in the summer of 2011, and the Serie A giants were given the option to buy the midfielder permanently for a set fee of €8 million [£6.5m].
However, Galliani has now revealed that they have no intention of meeting the Premier League side's demands as they want to renegotiate terms further down the road.
|Nesta among those leaving AC Milan
The 28-year-old Lopez moved to the Rossoneri in January, but has not done enough to convince Milan to retain his services.
"We are satisfied with what he has done, but we will not sign him. Maxi will return to Catania," Galliani confirmed.
The Milan director then stressed that his side are not interested in making an approach for Manchester City defender Aleksandar Kolarov.
"We have not made an enquiry for Kolarov," he claimed.
Milan have so far completed the signings of Riccardo Montolivo and Bakaye Traore.