Ole Gunnar Solskjaer has vowed to keep pushing and says Manchester United ‘will never, ever give up’, even if he concedes catching Premier League leaders Manchester City now looks unrealistic.

Having finished third and reached three cup semi-finals in his first full season, the Red Devils are safely ensconced in second heading into the home straight and have a Europa League semi-final against Roma to prepare for.

United are looking for their first silverware since winning that competition in 2017 under Jose Mourinho, with successor Solskjaer determined to bring trophies back to a club he won so many with during his playing days.

The 1999 treble hero believes the side are on the right track but admits adding to their 20 league titles is unlikely this season, even if they cut the gap to leaders City to eight points by beating Burnley on Sunday.

‘Of course we’ll never give up,’ Solskjaer said. ‘Man United will never, ever give up.

‘This club has had too many setbacks and too many great comebacks to have that in our DNA, [giving up] is not in our DNA.

‘But if it’s realistic? No, probably not because when you’ve had a team so consistent as Man City have been, you don’t expect them to lose three games out of the last six.

‘But as long as we do our job, we know that we want to finish the season strong … so one game at a time.’

It would take quite a collapse to fall out of the Champions League spots, with the Red Devils on course to finish in the top four in back-to-back seasons for the time since Sir Alex Ferguson retired as champion in 2013.

‘You’ve got to make progress, step by step, and that’s just the reality,’ Solskjaer said.

‘Of course, if we can manage second place, if we can keep on winning and get second, if Man City win all their games or we win all our games, you want to finish the season strongly.

‘Of course, third last year, second this year if that’s what we manage and close to a trophy, it’s progress.

‘That’s not the end game. The end game is, of course, winning the league.

‘But we’re not in the era of Sir Alex now. We’ve had a transformation period since he left, which always would happen because there’s no one better. There never will be.

‘He was the boss. He was the one who stayed here for so many years, it was always going to be difficult to replace him, so it’s progress, step by step.

‘In the end, if we do that well enough, that’s when you get trophies and league titles, which is, of course, our ambition. That’s always got to be the aim.

‘But everyone knows what I am talking about anyway. It’s step by step.’

Solskjaer says United are ‘not a million miles away’ from the top – a belief furthered by the fact they have beaten Champions League semi-finalists Paris St German and Manchester City this season.

But now is about continuing to improve and that means beating Burnley, whose 2-0 win in January 2020 led the Old Trafford faithful to express their anger at the state of the club under the Glazer family.

‘The last three games, I think, against Burnley we’ve conceded two goals,’ Solskjaer said. ‘We’ve not won any of the last three home games against Burnley.

‘It’s a massive game for the players, massive game to show the mentality they have shown over the last 13 or 14 months.

‘Because I think the attitude has been spot on, the determination, the bounce-back ability, the quality of not letting one defeat derail your season or lose the momentum. Get straight back on getting points or a win.

‘The way they’ve coped with the whole situation, the players, I’ve got to say they’ve impressed me. I have said it many a time.

‘The coaches, the little details they try to improve on. I said the devil’s in the detail and our coaches, there can’t be too many coaches around the world that look into the detail as much as mine. I’m delighted to be working with them.’