He told
British national newspapers: "I got my real first taste of the Champions League this year and I thought I showed I can manage at that level.
"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."
Moyes said he has rejected offers of jobs, adding: "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. 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.
The 51-year-old said his next job might not be in England, explaining: "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. I will use United as an important experience in my managerial career. I feel I needed more time but I will use it to benefit me and help me in the coming jobs."