Italian champions have identified Montolivo as their priority as Aquilani is pushed into the background by Galliani
Aquilani, 27, has been linked with a move back to Serie A as he currently does not figure in manager Kenny Dalglish's plans for next season following the arrivals of Jordan Henderson and Charlie Adam.
Talks were advanced between Aquilani's agent and Fiorentina but the move stalled as the player wanted a permanent switch in favour of the loan deal which was offered to him.
That impasse gave rise to speculation that Milan would be keen on bringing the former Roma man in, despite Allegri's chase for 26-year-old Montolivo, who wants to leave his current club after rejecting a contract extension offer.
Milan CEO Adriano Galliani has publicly stated his admiration for both Italy internationals, but Goal.com understands Montolivo takes precedence over Aquilani.
A Milan source told Goal.com the San Siro giants have made enquiries for the Liverpool playmaker, but is currently seen as more of an alternative to Montolivo.
"Regarding Milan's interest in Aquilani, there was a phone call between Adriano Galliani and the player's agent Franco Zavaglia," the source said.
"Galliani told the agent Milan like Aquilani and feel he is a good player, but said he doesn't fit in with Massimiliano Allegri's technical project for the squad for next season.
"Thus Aquilani is not seen as being a player who would suit the plans, more likely as an alternative [to Montolivo]."
Allegri has admitted that Montolivo is a player who would suit Milan's requirements to play a centre-left role in midfield.
However, Fiorentina have reportedly already rejected two Milan offers for the Italian, including a €6 million cash deal plus half of forward Alberto Paloschi's rights.
The other offer was a deal apparently involving Antonio Cassano, who has been told he will start the new season as fourth choice up front for the Scudetto holders.
For his part Aquilani is likely to leave Liverpool this summer but his €4 million per annum wage demands could put a limit on his options.
Aquilani is keen to hold down a regular slot for Italy ahead of Euro 2012 and knows staying at Liverpool without the guarantee of regular action could scupper his hopes of appearing in Poland and Ukraine next year.
Reports on Tuesday claim Juventus may be interested in bringing him back, but they have signed Andrea Pirlo and Arturo Vidal in preference to taking Aquilani on a permanent basis following his loan spell in Turin last season.