Moyes was at the helm of Goodison Park from 2002 to 2013 and managed to take Everton to a fourth place finish in the top flight in the 2003/04 season, playing Champions League football the following season.
The 58-year-old, with current club West Ham, is just three points adrift of a top four finish this season and has five games left in the campaign to once again lead a team into the Champions League.
Moyes revealed he would consider his spell at West Ham to be successful if he manages to turn them into a side that challenge the top teams regularly like he was able to do at former club Everton.
The Hammers boss believes the best is yet to come from him as a manager and admitted winning silverware somewhere down the line is also on his mind.
“I’ve always thought this but maybe my best time is still to come, why should I be old?”, Moyes told the Evening Standard.
“Maybe I’ve only just come through my apprenticeship.
“Maybe the jobs I’ve had have just been my apprenticeships and this is me getting to an age and experience where I can give my best.
“I’m saying to myself, ‘This is the time you get success, you win and get around the top of the league again’.
“I see this as a chance to work my way back. And [at] West Ham my job is to work my way back to a level where big clubs might consider me.
“Not that I’m interested in leaving any more, I’m happy.
“But I wouldn’t have got that [opportunity at Manchester United] if I hadn’t done my work at Everton, regularly challenging the top teams.
“If I can do that at West Ham, I’ll see it as success for West Ham and for myself. I’d love somewhere along the way be someone who wins trophies.”
West Ham are set to lock horns with Burnley at Turf Moor on Monday in their next league outing, while his former club Everton are also chasing a European spot finish under boss Carlo Ancelotti