Solskjaer, who Manchester City rejected back in 1996, is backing Alex Ferguson and his players to keep their noses in front of City for the foreseeable future.
After an 11-year career with Manchester United, Solskjaer knows a thing or two about derby games and he was quick to give a withering assessment of the noisy neighbours' remarkable transformation from a club in chaos to one to of the richest on the planet.
"It's always this thing about being the big brother and the little brother coming to try to overtake the big brother," he claimed.
"That always happens in families and in clubs - the young player hoping to take the old player's position. City are hoping to overtake United. I don't think they'll ever be able to."
Currently managing Norwegian outfit Molde, Solskjaer believes that resilience is the key component which has made Manchester United great.
"When you get disappointments, you bounce back. The start of this season has been good, not brilliant, but United are always improving throughout the season," he said.
"Man United have over the years - and through their history - won in dramatic fashion. In the club's history, you've had so many disappointments, like the Munich air disaster, and they have always stood up again and bounced back. It's just in the DNA."
Ryan Giggs added his voice to Solkjaer's by playing down the scale of the Manchester derby and claiming that Liverpool and not Manchester City are Manchester United's biggest rival.
"It doesn't mean anything extra because it is City," said Giggs.
"There are different rivalries. Liverpool has always been the biggest rival for me. It has always been the biggest test.
"Arsenal were a brilliant team and we had some ferocious battles with them. Chelsea were also a brilliant team under Mourinho and now City are a good team as well.
"The added dynamic is that they are on our doorstep. But we still want to win the league no matter who we are competing against."
Yet, whilst Giggs agrees with Ferguson's assessment that Chelsea cannot be written off, after losing out on goal difference to a side they failed to collect a single point off in their two meetings last term, the Welshman is aware how significant Sunday's game can be.
"We have found over the last couple of years that the derby, with the money City have spent and the quality they have brought in, has got bigger and bigger," said Giggs.
"The two games against them were the difference last season. Hopefully we can get the right result and that will be the difference come the end of this season."