The Red Devils were held to a 1-1 draw with Huddersfield Town in their penultimate Premier League fixture of the season.
Manchester United’s failure to beat Huddersfield ensured that they can’t catch fourth-placed Tottenham with one game to go.
Solskjaer took over the reins from Jose Mourinho back in December before the Red Devils made Solskjaer their permanent manager at the end of March.
The Norwegian head coach is bound to be linked with a host of players as the ex-striker looks to stamp his authority on the 20-time English champions.
The Red Devils have a number of key players, such as Ander Herrera and Juan Mata, who are set to become free agents in the summer unless the pair sign extensions in the final weeks of the season.
Speaking at his post-match media conference after Manchester United’s disappointing 1-1 draw with Huddersfield, Solskjaer said:
“We’ve talked about next season as in we need to start to rebuild and of course next season will be one without Champions League football – that’s a challenge in itself, playing on Thursdays.
“We’ll see how we cope with that. It’s a big summer.”
Manchester United have only managed to finish in the top four on two occasions in the past six Premier League seasons.
The Red Devils lost in the quarter-final stage of both the Champions League and the FA Cup this season.
Manchester United haven’t won the Premier League title since 2013.
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