Although he is the fourth-longest tenured manager in England, many believe the Scotsman is destined for a spot as the Manchester United manager when Sir Alex Ferguson steps down following next season.
Of course, Moyes is one of several who have been targeted for the for the job. It is hardly guaranteed that he would land the position. One thing working against Moyes is his recent inability to get the most out of his team at the beginning of the season.
Both this season and last Everton has started out of the gate very slowly in the Premier League. They currently find themselves 15th on the table with 17 points, only five points out of the bottom spot. On the other hand, they are only six points from sitting sixth on the table.
Moyes is hardly thinking about the United job right now, as he focuses on trying to improve his club's standing heading toward the new year.
"My mind is on the next game," he told EvertonTV earlier in the week. "After you finish you look back and talk about them. When you are managing there isn't time to look back."
The 400th game as Everton manager was a big one for Moyes, as the Blues staged a late-game comeback to get a draw with Chelsea.
Only Ferguson and Arsene Wenger at Arsenal have been with their clubs longer than Moyes among the current 20 teams in the Premier League.
Moyes is trying to motivate a club that has underachieved much of the season and hopes he can build off that big draw with Chelsea. Everton will have to do without the services of perhaps their best player, Tim Cahill, come January, as the Australian will be playing with his national team in the Asia Cup.
Cahill could miss up to six games at the beginning of the new year.
Moyes, 47, is hoping to add some depth to the squad in the January transfer. He has already sent an offer out to Landon Donovan and the MLS, hoping for a temporary return from Donovan. The American is currently considering whether to return to Everton or take his first extended time off from the sport in several years.
With Cahill gone, Donovan would be a welcome addition to the midfield of the Toffees.
As far as Moyes replacing the legendary manager of United in a year and a half, that is something that he will not address at this time.
Jose Mourinho, Steve Bruce and Mark Hughes are a few of the other names being talked about as a Sir Alex replacement.