AC Milan insisted they have no desire to leave San Siro after the city's mayor raised the possibility of building a new stadium.
Co-tenants Inter have played their matches at San Siro since 1947.
Talk of a move away from the stadium erupted on Tuesday when Milan's mayor Giuseppe Sala claimed Gennaro Gattuso's side were considering their own stadium.
However, Milan swiftly denied those reports in a statement, which read: "In relation to the statements released by the mayor of Milan Giuseppe Sala, who stated that AC Milan has expressed the will to think about having their own stadium and that the City Council would have given the club time to consider alternative areas of the cities, estimating in two to three months the time-frame to find a summary of options, AC Milan states that the Club has never expressed the desire to leave San Siro.
"Although AC Milan considers important for its future to play in an owned stadium, therefore not sharing it with other teams, the decision on which can be the future sports facilities of the Milanese teams can be taken in adequate time and with full agreement of all the parties involved.
"It is for this reason that AC Milan, together with the City Council, have started a series of meetings and evaluating the areas available on the territory, taking into consideration the value of San Siro and the possible redevelopment of the stadium.
"Only at the conclusion of this path, all the parties involved will be able to express a full evaluation and eventually take decisions."
San Siro: la società risponde alle dichiarazioni del Sindaco di Milano, Giuseppe Sala https://t.co/QD5PPHlNuG— AC Milan (@acmilan) January 9, 2018
Sala, who spoke to Sky Sport Italia , responded via Twitter, saying: "I note Milan's statement on San Siro. Let's just make this simple: I think that for Milan, for the fans and the tourists, the stadium needs to be modernised.
"When will Milan be able to tell me if they are available or not to invest along with us in our stadium? Let it be clear, the invite also goes out to Inter, because this is the stadium of Milanese people."
Inter – third in Serie A and 14 points above 11th-placed Milan this season – also weighed in by replying to Sala's tweet.
"Dear Sala, as you might recall, we invested time and resources in the stadium of Milanese people. Our plans have been clear to everyone and have not changed for 18 months," Inter said on Twitter.
"We await a round table discussion with all the actors involved to speak about this with clarity."