The Toffees are once again on the hunt for a new manager after Roberto Martinez's sacking on Thursday, with Moyes quickly installed as one of the favourites for the job.
When asked whether he would be open to a dramatic return, Moyes said:
"Would I consider going back? I've said if I get an exciting challenge and something that makes me feel I could get my teeth into it then I would be really interested.
"When we took over we had 11 great and successful years but we also had to rebuild the club a little bit. I just think now the change has been made and Everton need to now go and do it again.
"If you give David Moyes an opportunity he tends to rebuild a club and he tends to get it going in the right direction and making sure that things are correct and I'm looking forward to getting the chance to do that again."
Moyes has been reported as recently as a few weeks ago to be desperate for a return to coaching at Goodison Park.
The Scot spent 11 years in charge on Merseyside, joining in 2002 with the club struggling at the bottom of the table, up to their eyeballs in debt and with an ageing squad.
Moyes slowly managed to rebuild the side and transform it into a resilient outfit regularly finishing in the top eight of the Premier League, despite operating on a shoestring budget.
When Sir Alex Ferguson retired in 2013 Moyes, who had allowed his contract to run down at Goodison, was appointed his successor. The majority of supporters were disappointed to see him leave but felt that a change was good for both parties, with Moyes' rigid style of football beginning to grate with some.
That's why a return to the Toffees hotseat would feel like a step backwards for all concerned, though there is part of me that wonders how he would get on with substantial funds to play with - Moyes regularly had to sell-to-buy during his first spell in charge.
After the frustration of the Martinez era the fans are also looking for a name that will galvanise the club, give everyone a lift and stoke some excitement. I'm not sure David Moyes would do that.
Here is an analysis we did of whether Moyes would be a good choice or not to return to Everton as manager.
Is David Moyes the answer for you? Have your say in the comments below!