With second-placed Manchester City facing a European ban for breaching UEFA financial rules, fifth would guarantee qualification for the Champions League unless City win an appeal in the Court of Arbitration for Sport.
"I don't think the club would panic or go crazy with plans that we've already talked about for years to come," Solskjaer told reporters in a virtual news conference ahead of Monday's Premier League home game against 12th-placed Southampton.
"You do have to have a long-term plan but short-term some decisions will be easier to make if you get the Champions League."
Kai Havertz is ‘better than Cristiano Ronaldo’… and Chelsea are close to getting him – Euro Papers
United could also qualify for the Champions League by winning the Europa League, where they hold a 5-0 advantage over LASK heading into the second leg of their last-16 tie.
United, who are on a 17-match unbeaten run in all competitions, have won each of their last four Premier League games by three goals and Solskjaer said attacking football was ingrained in the club.
"It's about winning, of course it is, but it's also about our fans and the way we approach the game. You play with pace, power, you play with no fear, you take risks and you've got players who have got quality," he said. "That's just the DNA of the football club."