United booked their place in the last four for the first time since winning the competition in 2017 with a routine 3-0 victory over League Two outfit Colchester at Old Trafford on Wednesday.
Strikes from Marcus Rashford and Anthony Martial, as well as an own goal from Ryan Jackson was enough to get the Red Devils over the line and their reward for making it through to the semi-finals is a showdown with their near neighbours.
United have good recent memories of facing City, as they claimed a 2-1 Premier League victory at the Etihad Stadium earlier this month, while they also beat the Citizens the last time the two sides met in the Carabao Cup back in 2016 - Juan Mata scoring the only goal in a 1-0 win.
Solskjaer is certainly not afraid of taking on the two-time defending champions, although he is also full of respect for Pep Guardiola's side, who have dominated the competition over recent years.
"[They will be] fantastic days in Manchester," Solskjaer told United's official website. ";Of course, we do really respect them and, as I said after the derby last time, in my opinion, they are the best team in England.
"They can out-football you so we need to get our game heads on and be ready for them again. But we've shown them that we can cause them problems. I think they will be two fantastic games."
The first leg of the tie will take place at Old Trafford the week commencing January 6, with the return match coming three weeks later at the Etihad Stadium.
The winner over the two legs will go on to face either Leicester or Aston Villa in the final at Wembley on March 1.