The Brazil international is a top target for Juventus amid claims he has become frustrated over his lack of first-choice status under Guardiola.
However, the City manager is adamant Gabriel is not for sale this summer.
A club source told The Sun: "Gabriel is not going anywhere!
"He never gave the club any indication that he was not happy here in City. He is not one of the club's biggest employees, but when the time comes, the club plans to recognize his high status on the team and on the international stage."