City have reached an agreement with the J-League side over the young forward's signature.
The 21-year-old currently doesn't have the requirements for a work permit meaning a loan to another European side is likely if the move gets confirmed.
Meshino has already travelled to Europe for his medical.
Gamba manager Tsuneyasu Miyamoto tried hard to keep the 21-year-old, but he expressed a strong desire to play in Europe and the club decided to let him leave.
“We prioritised his feelings," said sporting director Masanobu Matsunami.
Gamba have confirmed the transfer on their website in the last 24 hours.