"For Man Utd you should always aim to win the league," he told reporters ahead of Tuesday's league clash against Burnley.
"We can't do that this year, but we have to get back to the challenge. We've got the Champions League, we've got the FA Cup, we can't just say we've got top four and that is it."
United's last trophy - the Europa League - came in 2017 but they have not won the Premier League since former coach Alex Ferguson's final season at Old Trafford in 2012-13.
Although Solskjaer admits a league title challenge is unrealistic this season, he backs the squad to catch Tottenham Hotspur, who are seven points ahead in third place.
"We are sixth at the moment, so we are a way off the top teams. We are challenging to be top three at the moment," the Norwegian added.
"It's about reorganising and just starting next season to be ready to challenge and get more points."
United will play defending champions Chelsea in the FA Cup fifth round on Feb. 16, four days after they take on French champions Paris Saint-Germain in the first leg of the Champions League last 16.
(Reporting by Hardik Vyas in Bengaluru; Editing by Amlan Chakraborty)
