Donovan said this week that he had instead chosen to give his body time to rest and recuperate following two straight years of football.
Moyes said at his press conference on Thursday: "There was always more than a glimmer of hope. If he was going to come anywhere, it was going to be Everton.
"I knew he wanted a holiday, I spoke to him maybe two weeks ago and I thought that normally you would be saying, 'I'm going away on holiday and I can't wait to be back'.
"But he had the loan spell with us, the World Cup then the MLS, it is a hard ask but he would have hit the ground running because he knows how we work. We will have to look elsewhere.
"He phoned me and said he needed to give his body a rest. I understand his views and he said he might pop over and say hello to us next year!"