The Red Devils are seemingly progressing under Solskjaer, currently sitting second in the table and still in contention in two cup competitions.
However, they are not really in a race for the title, with Manchester City 14 points clear at the top of the table.
United are also in a spot of bother in the Europa League after only managing a 1-1 draw at home against AC Milan in the last 16, before a trip to Italy on Thursday.
On Sunday Solskjaer takes his team to the King Power to take on Leicester City in the quarter-finals of the FA Cup and Neville believes that it has emerged as a hugely important match for the club.
‘The FA Cup has become critical to this football club this season,’ Neville told Sky Sports. ‘The League Cup and FA Cup has been the starting point for Manchester United teams over the last 15 to 20 years.
‘If Ole Gunnar Solskjaer is going to be successful at this club, he not only needs to finish second in the Premier League, but he has to win a trophy.
‘That would be seen as real progress. Then you’re attracting players next season to try and catch Manchester City.’
Solskjaer has lost four semi-finals as Manchester United manager so far, twice in the League Cup, once in the Europa League and the FA Cup.
He needs to improve on this record, according to Neville, for this campaign to be judged a success.
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