The Red Devils' legend cannot see his former club's global position being outdone, while he thinks their three-point lead in the league will help them relax in the derby on Sunday
Sir Alex Ferguson's men travel to Etihad Stadium on Sunday with a three-point advantage over Roberto Mancini's side at the top of the Premier League table.
City recorded a league double over United last season on their way to the title, including an emphatic 6-1 victory at Old Trafford, but Solskjaer feels that despite their success they are still a long way behind the Red Devils.
"There's always the big brother aspect, when the little brother tries to overtake the big brother, it always happens in families, in clubs where a young player wants to overtake the old player's position," he told reporters.
"City are hoping to overtake United but I don't think they'll ever be able to."
The league-leaders have been criticised for their defensive play this season after conceding 21 goals in 15 Premier League games, but Solskjaer believes it is his former team's nature to play entertaining, open football.
|10/1||Manchester United are 10/1 to draw 2-2 with Manchester City with bet365|
"Over the years Man United have always won in dramatic fashion," the 39-year-old told reporters.
"Over the club's history we've had disappointments and it's always stood up again and bounced back because that's just in the DNA.
"I think Man United will relish those games, going there knowing it's not a decider. You can go there try and dominate the game with the players.
"Van Persie, that signing has been successful already. Maybe you want to wait a year or two to see if it will be a success but you already know it's a success."