Yet when the two sides face each other at the San Siro on Sunday in the first part of a double bill, which also features a Italian Cup game three days later, it will be Lazio in the role of favourites.
Lazio go into the match in third place with 46 points and as Serie A's top scorers, having blasted 56 goals in 21 games, including six matches where they have scored four goals or more.
Milan, meanwhile, are stuck in seventh place with 15 points fewer than their Lazio, despite having spent almost 10 times as much as their opponents in the summer transfer market.
"Nobody gave us much thought before the start of the championship," said Lazio coach Simone Inzaghi after Wednesday's 3-0 win over Udinese. "They expected to see us in 10th place but now everyone is talking about us."
"We must not forget where we started from. The lads deserve the praise but we can still get better."
Inzaghi, the younger brother of former Italy forward Filippo, was initially appointed on a caretaker basis late in the 2015/16 season.
Lazio then named Marcelo Bielsa as their long-term coach during the summer of 2016 but the eccentric Argentine quit after two days and Inzaghi, who had already agreed to coach lower tier Salernitana, was invited back.
Since then, the 41-year-old has emerged as one of the best young coaches in Serie A, taking Lazio to fifth place last season.
According to the specialist website Transfermarkt, Lazio spent just under 29 million euros ($36.01 million) in the summer transfer window with right back Adam Marusic the most expensive purchase at 6.5 million euros from Oostende.
Yet Lazio have a good track record of signings over the last few years with players such as Felipe Anderson, Sergej Milinkovic-Savic and Stefan de Vrij all rocketing in value since joining the club.
Milan, on the other hand, have spent 230 million euros on new players, according to CEO Marco Fassone, yet have been struggling for consistency ever since they lost 4-1 at Lazio in early September.
Coach Vincenzo Montella was fired in November and replaced by fiery former midfielder Gennaro Gattuso who, although he has a strong identity with Milan, had never coached a Serie A team before.
Gattuso also suffered a rocky start but Milan have enjoyed a mini-revival recently, beating neighbours Inter Milan in the Coppa Italia and winning their last two league games.
"This team has a lot of quality. I see great responsibility from the boys and a sense of belonging," said Gattuso after the 2-1 win at Cagliari on Sunday.
"The management could have done something in this transfer market but I asked them not to because I believe in this team. Some of our lads are very young and so many of our players can still do much more".
($1 = 0.8053 euros)
(Writing by Brian Homewood in Bern; Editing by Toby Davis)
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