The Scotsman spent 11 years at the helm of Goodison Park before being picked by Sir Alex Ferguson to succeed him at the home of the English champions.
"The transition from Everton to United has been difficult at times as I have hard decisions to make," Moyes told Inside United. "Everton are a great club and I was proud to manage them.
"I can't deny Manchester United are on another level. Let's be honest, it would be a step up from just about any club in the world."
United will take on Wigan Athletic in the Community Shield at Wembley on Sunday before kicking off their 2013-14 Premier League season the following weekend away to Swansea City.