Despite signing a two-year contract extension in November, Guardiola's long-term future remains uncertain amid a turbulent campaign.
City, who were initially set to see Guardiola's contract expire at the end of this season, have endured a disappointing year.
They have been eliminated from both the Premier League title race and the Champions League, raising concerns over the club's direction.
Their struggles prompted a drastic squad overhaul in January, bringing forward a planned summer rebuild in an attempt to turn their form around. The club also emerged as the biggest spenders in the winter transfer window.
However, results have not improved as expected, and City now face the real possibility of missing out on qualification for the 2025/26 Champions League.
This, combined with the team's continued struggles, has led Hamann to speculate that Guardiola may not see out his new contract.
"Well, when he signed the contract extension, I think that the contract was signed to calm things down and just bring a bit of stability into the club, because it was really needed at the time because of the 115 charges that the Premier League brought against City," Hamann said.
"You know, he's been there a long time. The people in charge of the football club are the same people that were running Barcelona when he was there, so they are not only colleagues, they're friends and I'm sure if he wants to go, they would find a solution.
"When I look at Pep this season, I'm not sure whether he's got [patience or energy] at the moment.
"It's a very testing job, being a Premier League manager. You have to transfer that fire from the manager to the players and make them believe they can win everything again. I'm not sure he can do that.
"I said that a few months ago. I'm not sure how far that time is where he says to himself, maybe somebody else is better equipped for the job. I'd be surprised if he's still the manager next season, regardless of where they finish."