Mathieu Flamini was offered an improved contract by Italian giants Milan.
The French midfielder’s deal is expiring, opening the door to a Bosman transfer this summer.
Earlier this month the club tabled an initial offer of a renewal, but, according to Mediaset, they’ve now increased their bid.
Flamini, 28, presently earns €4.5m at the club – only Zlatan Ibrahimovic nets more – but the Diavolo want to slash his wages by over 50 per cent.
According to reports, Milan are prepared to give the former Arsenal man a two-year deal worth just under €2m a campaign.
If Flamini accepts those terms then it is likely that Milan will not make an offer to Liverpool to keep Alberto Aquilani. The latter spent this season on loan at San Siro.