Solskjaer, 48, arrived at Old Trafford in 2018 as caretaker manager after the sacking of Jose Mourinho.
The United legend impressed during his caretaker spell and was appointed permanent manager on a three-year deal in 2019.
Solskjaer signed a new contract extension, which will keep him at Old Trafford until 2024, in July after finishing second with United and reaching the Europa League final last season.
Now, Solskjaer's long-term future at United could entice Haaland, who worked under the Norwegian during his time at Molde.
According to The Daily Mirror, Haaland turned down the chance to sign for United after he left RB Salzburg for Dortmund.
The newspaper claims that the 21-year-old Norwegian striker 'feared' Solskjaer's future at United wouldn't last for the long term.
Haaland was reportedly wary of how United had axed the likes of David Moyes, Louis van Gaal and Mourinho in the post-Sir Alex Ferguson era.
The Mirror reports that the Dortmund star was 'worried' about how his future could suffer if he moved to Old Trafford.
However, Solskjaer's new contract extension and United's summer transfer investment could lead to Haaland reconsidering his position.
United splashed out a whopping £73m to land Haaland's former Dortmund teammate Jadon Sancho this summer.
Raphael Varane is set to become Solskjaer's second major signing of the summer after United agreed a deal for the Real Madrid star.
Edinson Cavani will remain at United for another season, but the Red Devils will be keen to invest in a long-term successor for the 34-year-old Uruguayan striker.
Chelsea and Manchester City have been heavily linked with Haaland, but Dortmund remain firm on their staggering valuation of £160m.
But Dortmund face a tough test in keeping Haaland, with the Norway international's £68m release clause becoming active in 2022.
Featured Image Credit: PA
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