Serie A champions are still seeking to strengthen their midfield but their budget may not extend far enough to prise the Italian international midfielder away from Anfieldhere.
AC Milan are keen not to let Liverpool's Alberto Aquilani slip through their fingers, but they are reportedly unwilling to meet the €10 million (£8.7m) asking price set by the Anfield outfit.
On Friday Aquilani's agent, Franco Zavaglia, left the door to the San Siro open after he said a move there should not be excluded.
And La Gazzetta dello Sport claims Milan have revived the embers of interest in the 27-year-old midifielder, who scored the winner in Italy's 2-1 win over Spain on Wednesday.
However, CEO Adriano Galliani is not keen on spending more than €6m (£5.2m) for the Italy ace. Liverpool are believed to be holding out for at least €10m, but budgetary contraints are preventing Milan from paying that amount.
Meanwhile, Fiorentina's Riccardo Montolivo is thought to remain as the Serie A champions' ultimate target.
He tried to play down reports of an exit earlier this week, but the Florence outfit are reportedly looking to offload him for €10m after he refused to sign a new deal last month.
Both midfielders appeal to coach Massimiliano Allegri who has made no secret about wanting to sign a top-class player for the centre-left side of the pitch.