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Ole Gunnar Solskjaer led United to second place in the Premier League last season and ensured Champions League football for the upcoming campaign.
However, the 48-year-old Norwegian's hope of capturing his first piece of major silverware as United boss were dashed with Villarreal's win in the final of the Europa League.
United have strengthened this summer and completed their sensational £73m acquisition of Jadon Sancho from Borussia Dortmund.
The Red Devils have also reached an agreement with Real Madrid to land Raphael Varane, who is set to undergo his medical before finalising his move to Old Trafford.
Joining Sancho and Varane at United ahead of the new season includes former Burnley star Tom Heaton, who has returned to Old Trafford on a free transfer.
Hamann believes that Sancho "will improve" United, but their defeat in the Europa League final will "put doubts in people's minds."
The former Liverpool and Manchester City player went on to praise Leicester under Rodgers and believes the Foxes will "climb above [United] for the top four."
Speaking to British Gambler, Hamann said: "I'm not sure Manchester United are guaranteed a top-four berth, I heard someone say on the radio that Ole Gunnar Solskjaer wouldn't get a job at any other top club and that he's got plenty to prove.
"That wasn't them being disrespectful, it was merely making a point and a fair one, in my opinion.
"Jadon Sancho will improve them, but I don't think they have a base and losing the Europa League final to a team they should have beaten will continue to put doubts in people's minds.
"I'd suggest Leicester will climb above them for the top four, they've been narrowly pipped in each of the last two season and Brendan Rodgers will ensure they go again.
"They look completely at home at elite level, Youri Tielemans is a class act in their midfield, they are full of goals, have a solid defence and I don't see them taking a backward step compared to Manchester United."
Featured Image Credit: PA/Manchester United
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