"The two clubs said no to the restructuring of San Siro proposed by (construction group) WeBuild," Sala said after a meeting with officials of the two northern Italian clubs.
"They provided detailed analyses of technical and economic feasibility and their conclusions are that this project cannot be carried out at a sustainable cost and that they do not wish to move in this direction."
The two clubs would, however, be ready to relaunch the initial project of a new stadium in the immediate vicinity of San Siro, according to Sala.
"We are not starting from scratch on this subject, but there is resistance from local residents," Sala pointed out.
"They must present us with a project within a fairly short time frame, but building stadiums in Italy is never easy, it is always very complex."
To increase their commercial revenue both clubs, who have been crowned European champions 10 times between them, have announced that they wish to leave the San Siro, which is owned by the city of Milan.
Officially known as the Giuseppe-Maezza stadium, the 80,000 capacity San Siro is a spectacular concrete structure built in 1926 but which no longer meets their needs.
The two clubs also each have a stadium project in their pipeline.
Earlier this year AC Milan bought land in the suburb of San Donato Milanese, to the south-east of the city, as part of a plan to move away from the San Siro and outside the official boundaries of the city of Milan.
Reigning Serie A champions Inter have their sights set on the towns of Rozzano and Assago, just south of Milan, after having also sounded out the possibility of building on former industrial land in populous northern suburb Sesto San Giovanni.
In 2026, San Siro will host the opening ceremony of the Milan-Cortina Winter Olympics.
It should also be the scene of the 2027 Champions League final, which according to the Italian press could be called into question amid the ongoing uncertainty over the stadium's future.
