The Red Devils are heading into a 7th year without being any closer to winning the league title since Sir Alex Ferguson left in 2013.
But now, Manchester City are two-time defending champions and have won four of the last eight Premier League titles.
when Solskjaer was asked if he still regarded United as the bigger club, he replied: "Yeah."
Solskjaer, whose sit currently lie sixth in the standings, a distant 11 points from their rivals and eight away from the Champions League spots, is still confident that United will ultimately get things right.
“With the size of our club, we're going to have to bridge that gap, and our aim is to go past the teams above us,” he said.
“I believe that's what we have to aim for, that's we have to go for and that's what we have to believe in, because we do have the resources to do it, we do have the people to do it, so why not?
“As long as we're going in the right direction and we get there, that day when we do is going to be a very good day.”
The Norwegian also rejected the school of thought that City’s spending power means that they will simply dwarf United in that regard.
“I don't agree,” he added.
“What are you going to do? Are you going to give up? Not challenge them? That's what we've got to get back to.”
City won both derby encounters in the league last year, with their 2-0 success at Old Trafford in April considered to have been a big hurdle cleared en route to winning the title by just a single point over Liverpool.
Confirmed Manchester United Squad:
Goalkeepers: David de Gea, Lee Grant, Sergio Romero
Defenders: Aaron Wan-Bissaka, Victor Lindelof, Harry Maguire, Axel Tuanzebe, Luke Shaw, Ashley Young, Brandon Williams
Midfielders: Scott McTominay, Fred, Andreas Pereira, James Garner, Jesse Lingard, Juan Mata
Forwards: Daniel James, Anthony Martial, Marcus Rashford, Mason Greenwood,