The Verona-based company has stumped up €100,000 to fund the international competition, which invites ideas on how to equip the iconic venue with a roof that is both retractable and removable.
Calzedonia's founder and CEO, Sadro Veronesi, said the aim was to protect the first century arena from the being worn away by rain and pollution.
“Our primary objective is to find ways of protecting one of our greatest cultural treasures which is suffering irreparable damage from exposure to atmospheric elements,” Veronesi told Il Sole 24 Ore.
But the potential addition of a roof to the structure could also offer considerable economic benefits to Verona.
Currently the largest open-air opera venue in the world with a capacity of 15,000, the theatre can only stage a short season of shows during the summer months. Even then, both performers and the audience are at the mercy of the elements.
“A roof would allow shows to be put on all year round, which would be a great advantage to the city and we hope that many people take part in the contest,” Veronesi added.
Some €40,000 will be awarded to the winning design, while €20,000 be awarded for second place and €10,000 for third. Some €30,000 will also be paid to the jury.
While the primary contest does not guarantee that the project will be realized, winning groups will most likely be heavily involved with any future roof construction projects.
The privately-funded contest is just the latest example of Italian companies stepping in to finance heritage projects which the country's cash-strapped government can ill afford.
Last year, an extensive refurbishment of Rome's Trevi fountain was completed by the fashion house, Fendi, while the city's iconic Spanish Steps are being given a Bulgari-funded makeover.
“We thank Calzedonia for their sensitivity to the city of Verona and it's most important monument," Flavio Tosi, the mayor of Verona, said.
"The amphitheatre is unique worldwide and plays a central role in the socio-economic life of our city.”
The contest will run from March 18th to September 9th and is expected to attract architects, engineers and specialist groups from around the world.