The club's board had continued to back the Norwegian, but Saturday's 4-1 defeat at Watford in the Premier League led to the treble-winning striker being relieved of his duties.
Solskjaer has revealed that he will now return to Norway to be with his family but is planning to return to working in football at some point in the future.
"I'll spend some time with my family. That's been probably the most difficult part, through the pandemic, with Norway being open and here being closed, my family moved back to Norway and the young one, he loves it back there, so we've lived apart," Solskjaer told MUTV.
"So, I'll spend some time with them. Then, I'll watch the team of course and hopefully, the next manager comes in and I want to support him.
"I want him to be successful, hopefully I've laid the foundations for that to happen because I know I'm good at what I'm doing. I'm 100% sure to create a football environment, that's where I'm good at and at some point, I'll probably be back [working in football]."
The 48-year-old took charge of 168 matches for the Red Devils between December 2018 and November 2021, boasting a record of 91 wins, 37 draws and 40 defeats.