But, the manager has seen the early push vanish, with the club recording just 2 wins in their last 10 matches in all competitions.
Last season José Mourinho's side finished second but 19 points behind City, while United were 27 points behind the champions and 26 from Liverpool at the start of this weekend. "We've been working on creating chances and scoring again".
He said: "I have regular meetings with Ed [Woodward, the executive vice-chairman], I've seen Joel [Glazer, the cochairman] and the [other] owners: they are very realistic on where we are and what we want to get to and how long that will take".
Solskjær believes a failure to qualify for the Champions League would not dissuade elite players from joining United.
David De Gea, the out-of-form goalkeeper, has committed a number of errors of late, but he will keep his place in the team because his understudy, Sergio Romero, suffered a knee injury in training this week.
Whether they get there or not is another question but the former striker has stressed that despite the uncertainty on the club's European future, both players and agents have approached the club - in their numbers - regarding potential transfers this summer.
"You have to perform at Man United and to perform you've got to really work towards that dream and that's what we're doing every day as a staff".
The injuries have piled up for Ole Gunnar Solskjaer, who is in a precarious situation, especially in attack, with Marcus Rashford, Romelu Lukaku and even Mason Greenwood either injured or doubtful to make the team on Sunday.
"Yes, we're having a tough time at the moment". We're supposed to be signing 250 players!
Yes, we have had a few seasons that haven't been up to the standards we expect, but players still want to come to Man United.