Argentinian Willy Caballero has been chosen ahead of Hart for the opening Premier League and Champions League matches this season and is expected to stay in goal for Saturday's game away to Stoke City.
"I want happiness for the players," Guardiola told reporters in his pre-match news conference.
"I don't want players to stay if they don't want. They decide the future, because they have a contract.
"I said to him that if he stays, he's going to improve, to understand what we want from our goalkeeper."
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He said Caballero had been picked because he had more time in pre-season than Hart, who was involved in the European Championship.
"Willy played these two games and right now is better. But that doesn't mean Joe isn't going to play.
"I have a lot of respect for him. I know his value. I was clear what I was looking for."
Asked what he wanted from a goalkeeper, Guardiola replied: "First thing I look for is saves. But after, he has to play with the ball, help us create a good build-up."
Guardiola, who joined the club from Bayern Munich in June, said he had in the past had many players who "had problems" but stayed and improved.
He cited former Barcelona defender Eric Abidal, "who in the end became the best left-sided central defender in Europe," with the Catalan club.
"If Joe stays here he will fight with the other keepers and will convince me to play. That is the way it is - nothing has changed."
Midfielder Yaya Toure has also been left out of the opening games and Guardiola said he needed to work harder off the ball.
"Yaya is trying very well, he loves football. I spoke with him about his situation, he’s a player with huge quality.
"I have adulation and respect for Yaya’s quality. When he increases his intensity without the ball, he will be involved."
(Reporting by Steve Tongue, editing by Neil Robinson)
