Ahead of a derby clash with rivals City at Old Trafford on Wednesday, United are 24 points behind leaders
United have not won the Premier League since Alex Ferguson retired in 2013 and Solskjaer is uncertain over how competitive the Red Devils can be in 2019-20.
"I don't think we've got the consistency to do that," Solskjaer told reporters when asked if United can fight City and Liverpool for the title next season.
"Over the last 18 games, we're not far away from them but it's doing it over the course of a season. We've done it for half a season now. Let's see. You can never say never.
"You cannot expect things to happen overnight and we know that. It will happen gradually and we have to be realistic enough as a club that we have to take it
"That's not changing 10 players now and bringing 10 players in. It's slowly, slowly but surely. It has to be the right quality,
United fans have been left to weigh up whether they would rather see neighbours City or equally fierce rivals Liverpool be crowned champions.
"It's not about taking something away from others," Solskjaer added. "We have to want to overtake them, and not just because it's City and Liverpool.
"For a supporter, as I am, and as a manager now as well, we know [them well] because they are so close in the vicinity.
"We want to be the best, we have been the best and it's not nice seeing those two at the top."