United have not won the league title since Sir Alex Ferguson’s final season with the club in the 2012/2013 season.
The Old Trafford outfit have taken runners-up spot in the top flight just once since then, in the 2017/2018 season when they finished 19 points behind champions Manchester City, with then-manager Jose Mourinho describing it as one of the biggest achievements in his managerial career.
United look set to finish second once again this season, as they currently sit 14 points behind runaway leaders Man City with eight games left.
Ahead of Sunday’s trip to Tottenham Hotspurs, where they will come face-to-face with Mourinho, Solskjaer has asked his side not to be content with their current position on the table.
"You can’t say that is an achievement," Solskjaer told reporters when asked about the merits of finishing second.
"Our ambition is a lot more than second place. I said that when I wasn’t at the club – you can never be happy with that and we’re not.
"Don’t get me wrong, our ambition is to catch the team in front of us.
"At the moment [City] have had a fantastic season, they have had three or four of them, and we know the challenge ahead of us. But we have to take it on. If you don’t, then you’re in the wrong place because that is what I am going for.
"Players have to really take that on with the sacrifices they have to make and the work they have to do. Blood, sweat and tears have to be put down because this is the best league in the world – and the most difficult."