Moyes was interviewed for the Aston Villa job last week but has ruled himself out of the running.
Villa are currently in the hunt for their next manager having sacked Remi Garde earlier in the campaign.
A number of names have already been linked with the job, as the club take their time to make the right appointment.
Moyes was among those reportedly on a three-man shortlist being considered and was in fact interviewed by the club last Thursday night.
However, he has now dropped out of contention for the job, with BBC Sport reporting that he has decided against it after thinking about it over the weekend.
With Moyes now out of the reckoning, it will be interesting to see who the other candidates for the role prove to be.
Former Leicester City manager Nigel Pearson has been heavily tipped since Garde’s departure, while Roberto di Matteo is another name that has been linked with the position.
The Italian was reportedly in talks with Lazio last week though, and the Villans will have to move quickly if he is the man they elect to take charge.