Solskjaer has enjoyed success as a manager in Norway, having led Molde to their first league trophy in 2011, and he has already attracted interest from several English clubs including Aston Villa.
He opted to stay in Norway after talks with Villa in the summer, but he says he has ambitions of managing in England one day, with the United job his big goal.
"I'm not naive enough to say I can do that job but in life you should have big dreams and big goals," said Solskjaer, who joined United from Molde in 1996, in The Sun.
"It's a dream but let's take just one step at a time. I want to become a manager in England.
"At the moment I've just started and it's been two years more or less in Norway. So the time will come. I've spoken to clubs and explained it's a bit early as I want to learn and don't want to jump too big a bridge at the start."
He continued: "Managing is not easy but it's very enjoyable when you are winning, it's challenging when you have a bad start.
"After playing at United the best players were always the best people - like Roy Keane, Ryan Giggs, Paul Scholes, Edwin van der Sar."