The musically minded visitor to Verona in July may have had the chance to watch Turandot, Aida or Carmen under the stars. But they may also have had to watch it under their umbrellas – or, worse still, not watch it at all.

Northern Italy is bearing the brunt of a wet and thundery summer in the bel paese that is flooding towns, emptying beaches – and, crucially, playing havoc with outdoor opera at the Verona arena.

But, determined to bring an end to the climatic vulnerability of his city's most lucrative monument, mayor Flavio Tosi thinks he has the solution that will protect the nearly 2,000-year-old Roman amphitheatre for good. He wants to put a roof on it.

According to Verona daily L'Arena, Tosi, of the rightwing Northern League, is planning to launch an international competition to draw suggestions for how the formidable architectural task should be addressed.

Francesco Girondini, superintendent of the foundation that runs the arena, says that of 25 recent evening performances, at least half have been affected by bad weather, with four cancelled and seven starting late or not finishing.

"I have always been in favour of announcing an international ideas contest for a possible cover for the amphitheatre," he told L'Arena. "The performances, taking place outdoors, have inevitably felt the effect of the bad weather this season. If a solution could be found that was compatible with the monument and the kind of performance that takes place there, we would be certain in our ability to put them on."

Tosi is reported to be convinced a detachable cover that fitted with the style of the building would be beneficial not only for the foundation's takings, but also for its structural strength. Dario Franceschini, Italy's culture minister, was quoted on Wednesday as saying he wanted to look into the issue further.

Reporting on the possibility, a journalist for La Stampa commented: "The project might seem either mad or unrealistic or both, but the mayor is very determined."