Sunday's 4-1 win at Bologna, where Beckham scored the first goal of his two-month loan from Los Angeles Galaxy, led the third-placed Rossoneri to openly start talking about the scudetto despite being six points behind leaders Inter Milan.
Wednesday's home game with in-form Genoa in fourth will be an important test of their ambition with a little over half the season gone.
Milan have not won the Italian championship since 2004 and despite losing to Bologna and Genoa in their first two games this term, the feeling is growing that they can catch a stuttering Inter.
"If we can always play like we have at Bologna, we can win the scudetto," coach Carlo Ancelotti told reporters as he celebrated 400 matches as Milan boss.
Kaka, whose world-record move to Manchester City collapsed last week, scored twice in Bologna to show why the Premier League club were so desperate to land him while Milan did well to fight back from a goal down.
SPECULATION RIFE
Midfielder Beckham, who has joined Milan to stay in the England reckoning during the U.S. close season, blasted in the fourth after a good move and speculation is now rife that he will stay in Italy beyond March despite his constant denials.
"Our wish is that he continues with us," Ancelotti said.
Milan's hopes of overhauling Inter and second-placed Juventus were boosted by patchy performances by the top two at the weekend.
Champions Inter were slightly lucky to beat Sampdoria 1-0 on Sunday and Juve were even more fortunate in winning 1-0 against Fiorentina on Saturday.
Inter travel to Catania, coached by former Inter goalkeeper Walter Zenga, on Wednesday with striker Zlatan Ibrahimovic back from suspension but defenders Cristian Chivu and Walter Samuel are carrying knocks. Coach Jose Mourinho was sent off against Samp.
Juve visit Udinese, who have failed to win in 11 league games, with Alessandro Del Piero in blistering form despite being substituted by Claudio Ranieri against Fiorentina and angrily throwing his coat and armband at the dugout.
