Solbakken at 52 is five years older than Solskjaer but they were in the Norway side that were once ranked number two in the world in the 1990s.
Solbakken also welcomed Solskjaer to FC Copenhagen when he was in charge for his first spell in 2011 and the former striker was learning the ropes as a coach.
However, Solbakken -- who won 58 caps -- said none of that got in the way of his planning in securing a second win in European competition over United.
Solbakken guided Copenhagen to a 1-0 win over United -- Solskjaer was in the team -- in the 2006 Champions League group stage.
He has now taken them to their first ever European quarter-final.
"We are friends from the national team in the 90s, where Norway was the second-best team in the world," said Solbakken at his eve of match press conference.
"You won't believe that! We were ranked number two in the world, so we played in a World Cup (1998) together.
"He took his coaching badge and I think he came to me before the last-16 against Chelsea in the Champions League in 2011.
"We have a good relationship. We are not close friends but I can say we are good friends."
'I'll keep the hair'
Solbakken -- who is back in Cologne where he coached the club for one season (2011/12) before a brief sojourn with another of the Europa League quarter-finalists Wolverhampton Wanderers -- would not be drawn as to whether he or Solskjaer was a better manager.
"I don't know who is the best but I know that he (Solskjaer) is now in charge of one of the biggest clubs in the world," said Solbakken, who returned to coach Copenhagen in 2013.
"At this moment in time it is difficult to compare us.
"As a Norwegian we should -- even me as a Liverpool fan -- be proud that we have a manager in one of the biggest clubs in the world and that he has been able to steady the ship and been able to put his authority into the club."
Solskajer for his part said he had enornmous respect for Solbakken.
"Well I've known Stale since... I played against him in 95, I've known him for years, he's had a very good career as a player, always the one we looked to stop playing, creative midfielder, fantastic coaching career," said Solskjaer.
"In a similar way he's had his ups and downs but really come through again and leaving a legacy at Copenhagen who are in the quarter-final for the first time.
"It's step by step. I went to Copenhagen to do my Pro License and they lost to Chelsea and hopefully this time they'll lose to us."
Solskjaer, though, was at pains to emphasise the match was not about their personal connection.
"First of all, it's not me and Stale," he said.
"We're not playing against each other.
"He's had a very good career. I've been a manager for almost 10 years so I'm not that new.
"It depends what you think is new. He is a bit older than me which you can probably see.
"I'm turning grey but hopefully I'll keep the hair (Solbakken is bald)."