Alberto did not show up for Lazio's preseason camp in Auronzo di Cadore, leading to widespread speculation over him possibly leaving the capital this summer, with Milan being the club linked the most.
According to a report from the latest edition of il Corriere della Sera (via MilanNews), the Spanish creative midfielder's agents have offered him to Milan.
While he is greatly admired by the Rossoneri, Lazio's asking price has put them off securing a deal.
Lazio president Claudio Lotito is evidently not happy with the current situation, wanting €50 million for Alberto if he is to leave the club.
This has led to the deal not being in line with Milan's philosophy over recent seasons, preferring to invest in younger players for cheaper fees, rather than going for large fees for experienced players.
Inter have the advantage of having former Lazio manager Simone Inzaghi at the helm, possibly helping to attract the Spaniard to the club.
Alberto could be enticed by a return to Spain, but it is highly unlikely that Villarreal would be willing to splash out so much money on a single player.
If Milan actually want to pursue the signing of Alberto, they need to try and act fast, with him being in high demand.
Lazio finished sixth in Serie A last season after suffering from a rough end to the season, with Alberto managing nine goals and providing two assists in 34 league appearances, mainly playing in central midfield.