Solskjaer wants trophies, not just top four, at Man United
Solskjaer has made an incredible start at the helm, winning all eight matches since replacing Jose Mourinho in December.
The run has pushed United back into the top-four race, with Solskjaer's side now just three points behind fourth-placed Chelsea.
But with his team still alive in the Champions League and FA Cup, the Norwegian said silverware was also a target.
"We've got the Champions League, we've got the FA Cup, we can't just say top four and that's it," Solskjaer said.
"We've got to look at 'can we win something this year?' and I go into every single game as a Man United manager thinking we can win this game."
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— Manchester United (@ManUtd) January 28, 2019
United's most recent trophy was the Europa League in 2017, while they are without a Premier League title since 2013.
Solskjaer said winning the Premier League should always be the goal for United, who are 16 points behind leaders Liverpool.
"That's not the dream though, to be top four. We're Man United – you should always aim to win the league," he said.
"We can't do that this year but we've just got to look forward to that again because we have to get back to that."
United look to continue their perfect start under Solskjaer on Tuesday, when they host Burnley.