Manchester United manager Ole Gunnar Solskjaer has refused to write off his side's chances of lifting the Premier League trophy this season but admitted it would be unrealistic to think about overhauling leaders Manchester City.

United, who are chasing their first top-flight title since 2012-13, can move to within eight points of Pep Guardiola's side if they beat Burnley on Sunday, with six games to play.

"Of course we will never give up," Solskjaer told a news conference. "Man United will never, ever give up. This team, this club has had too many setbacks, too many great comebacks to have that in our DNA.

"But is it realistic, no, because when you have 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 we want to finish the season strong."

United finished third last season, ending 33 points behind champions Liverpool and 15 points behind second-placed City. A top-two finish this season would spell progress, but Norwegian Solskjaer said his side had to aim higher.

"You have got to make progress and that is the reality," he said. "You want to finish the season strongly and if we manage second then it is progress.

"That is not the end game. The end game is winning the league. It's progress step by step and in the end if we do that well enough that is when you get trophies and league titles which is our ambition."

Solskjaer said forward Marcus Rashford remained a doubt for Sunday's clash due to a foot injury while Ivorian defender Eric Bailly, who missed the last four games after testing positive for COVID-19 during the international break, is in contention for a place.