The 22 year old impressed for Italy in their friendly against France on Wednesday despite the Azzurri suffering a 2-1 defeat, and Gregucci says he is ready to fight for a spot at City.
He told Sky Sport Italy: "Mario gave a great contribution (for Italy) and I saw in him the right attitude and behaviour.
"Mancini has chosen to give him a signal, and it is his right to make choices.
"Perhaps during the last week something was missing, but Mario is ready to take back the Manchester City shirt."
Gregucci added of his future: "Will he stay? It's not up to me to say. I just know that he is definitely redeemable. He has 22 years of talent and quality.
"He is a resource of our football club. He will give his contribution to the national team and to City."