The 24-year-old defender is part of the Italy squad going to Ukraine and Poland despite the fact he plays in Serie B.
"I am very proud to have such a great Toro player and really nice lad in the Nazionale," Cairo told Tuttosport.
"I hope he has a wonderful Euros and we all should be cheering on Italy, especially in such a difficult moment for our sport.
"As for Ogbonna's future, my only desire is to keep hold of him. I will make the right investments to keep the Coach happy, as Giampiero Ventura did so well this season and I'm very happy to be continuing this adventure with him.
"Ventura's new two-year contract is already prepared and we just need to deposit it with the Lega."