But the mayor said that he would keep his job until his contract expires next year.
Mr Pereira, formerly artistic director of the Salzburg festival and the Zurich Opera House, has brought millions in private funding to the opera house since his arrival for the 2014-2015 season.
It is the only way for La Scala, Italy’s leading opera house, to maintain a high level of artistic output, he has said.
The deal had included plans to open a music and dance conservatory in Riyadh, managed by La Scala’s academy.
The putative deal had been opposed by Matteo Salvini, deputy prime minister and leader of the nationalist, anti-immigration League party.
He said the opera house should remain “free and independent” and should not be tied to the Saudis.
Offers of largesse from other countries would be a different matter.
“If the Swiss want to invest in La Scala, we would not have a problem,” he said.