The Sun says Gunners boss Arsene Wenger is a big admirer of the Italy Under-21 star and wants to strengthen his defence when the transfer window reopens in January.
Ogbonna, 21, has been earning rave reviews in Serie B this season and is regarded as one of the best young talents in Italy.
He said: "I know exactly what I want and I am not closing the door on anything.
"My objective is to improve and reach the highest level. My first dream has been achieved and I have managed to make my professional debut.
"There will be time to see what the options are on other clubs."