United head into today's home game against struggling Burnley second in the table, 11 points behind City but with a game in hand.
The Norwegian believes his side are on the right track but admits adding to their 20 league titles is unlikely.
"Of course we'll never give up," Solskjaer said after his side wrapped up a 4-0 aggregate victory against Granada in the Europa League quarter-finals on Thursday, setting up a last-four clash with Roma.
"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."