Moyes led the Red Devils to the quarter-finals in the 2013-14 season before succumbing to Bayern Munich, though his failure to qualify for Europe's premier club competition for next season proved to be his undoing.
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Despite his sacking from United in April, the 51-year-old believes that he deserves another shot at the prestigious competition, be that with a Premier League outfit or overseas.
"I got my first real taste of Champions League this year and I thought I showed I can manage at that level," he told The Guardian.
"I would like somewhere that would give me a chance of being in the Champions League or a club that has ambitions of being in the Champions League.
"It could be at home or abroad. I have always liked the thought of broadening my horizons and learning a bit more and at the moment I am quite comfortable watching and learning.
"I will go away and learn and look again to see what is happening."
The ex-Everton boss has been linked with a number of jobs since being dismissed by the 20-time English champions, but has yet to return to management.
Moyes insists that is down to his own decisions and revealed he has already been approached regarding possible routes back into football.
"I have had a couple of opportunities to go back in and chosen not to do anything just now. I am going to look for what I feel is the right opportunity," he said.
"I would like to think I proved myself over the 11-year period at Everton and what I am capable of, and the level at which I want to manage."