The Norwegian was one of the most sought after strikers in Europe last month following his incredible form for Red Bull Salzburg, both domestically and in the Champions League.
The Athletic says the 19-year-old told Solskjaer and vice-chairman Ed Woodward that he had his heart set on pulling on the United jersey.
Solskjaer, having worked with Haaland at Molde, was keen on a deal and United chief travelled to Salzburg on December 13 to meet the player and was convinced they had wrapped up the deal.
That never came to fruition however, with Haaland eventually opting for an £18million move to Borussia Dortmund, where he has thrived - with 11 goals in his first seven appearances.
It is also reported that United's lack of Champions League football this season - and potentially next - proved decisive.