The winger had a productive 2020-21 season in the Bundesliga, scoring nine goals and assisting nine more.
Villa confirmed in a statement that an agreement had been made with Leverkusen, subject to him completing a medical and finalising personal terms.
The deal would involve City paying Villa £90m and a transfer of highly rated young winger Morgan Rodgers.
Villa would like to keep Grealish but sources have told ESPN that he would be allowed to leave if that was his decision.
Jamaica interntional Bailey joined Leverkusen in 2017 from Genk.