Leicester City and Chelsea currently occupy the positions, but Solskjaer thinks even ninth-placed Arsenal can still sneak in ahead of them.
Leicester have made a poor start since the Premier League resumed after an enforced pause amid the coronavirus crisis, drawing both of their league matches while crashing out of the FA Cup.
Chelsea have won all of their matches to move within a point of Brendan Rodgers’ side but Wolves – who have played a game more than their rivals are now within striking distance of both.
Solskjaer’s United can draw level with Wolves with a win away at Brighton on Tuesday night and would move seven points clear of Tottenham Hotspur in the process.
Sheffield United and Arsenal sit one and two points further behind them, but despite a nine-point gap between Mikel Arteta’s Gunners and fourth-placed Chelsea, Solskjaer still maintains they are in the hunt.
‘I think there are many teams for that battle for third-fourth [spot],’ said Solskjaer.
‘It’s exciting for fans, been waiting for football that matters, we want fans in the stadiums but at least now we can sit back and watch some exciting games.’
He added: ‘I think every year you’re in the Champions League is a great experience, for the players it’s a step forward.
‘For us it’s what we’re striving to do winning trophies and we need to focus on one game at a time and there are so many teams that want that place.
‘We can’t get distracted about looking too far ahead and onto the next one.’
With Manchester City facing a Champions League ban, it’s possible a fifth-place finish could be enough to qualify for Europe’s premier competition but the rest of the field won’t want to take any chances.
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