The 47-year-old, who joined from Preston in March 2002, guided Everton to eighth place last season and has taken them to as high as fourth during his spell in charge.
But speaking after Everton beat A-League newcomers Melbourne Heart 2-0 yesterday in a pre-season friendly at Etihad Stadium, Moyes expressed elight with the squad that will launch its season against Blackburn at Ewood Park on August 14.
"I think in my time at Everton we've now got as strong a squad as we've ever had so I'm looking forward to it (the coming season)," Moyes said after seeing goals from Jack Rodwell and Louis Saha.
"I'm looking forward to having a season with them and seeing how it goes."
But Moyes will not go public with any firm ambitions for the upcoming season.
"No, I'm not a great goal-setter," he added.
"I think you take the next game and you get on with it and you see where you end up.
"But we're ambitious and we want to do well and we've got a great desire to do better than what we've done in the past so we'll just try to keep it going and hopefully see where we end up."
Former Leeds striker Jermaine Beckford nearly scored with his first touch after coming on in the second half against Melbourne, and Moyes believes the new recruit could do well with Everton.
"I think that we needed a little bit more firepower up front and we've brought Jermaine in," Moyes said.
"Jermaine's just struggling a bit with his groin just now, he's not quite comfortable yet at training so we weren't going to use him but I felt we could get 20 minutes so I think he felt fine.
"And his first touch and his first movement nearly showed you why he's scored so many goals through the lower leagues.
"We're giving him a great opportunity to see if he can do it at the highest level."