James Tarkowski's 98th-minute stunned Liverpool last time these two sides faced each other and now the Toffees make their way to Anfield to try and put a dent in their title hopes. Moyes first gave some team news and started with defender Vitalii Mykolenko.
"We're hopeful that he will be OK but we still have to wait and see tomorrow exactly how he is."
Next, he moved on to Iliman Ndiaye and Dwight McNeil who have slowly returned to training.
"Both of them are coming on great. Illi is a little bit further on than Dwight at the moment but it is great that they are back in training.
"It's helped us a little bit with having Dom (Dominic Calvert-Lewin) out as well. Dom is the only one who is really behind it at the moment. We are just waiting on him coming back, but the rest are all getting much closer to fitness.
"He's not behind (his own recovery schedule) just behind the others who are coming back just now. I've not got a date (in mind) with Dom yet (for his expected return) but he's back and on the grass so good signs he is getting closer to it."
Moyes was then asked what he would say to Jarrad Branthwaite if he felt he had to leave the club to further his England ambitions after not being included in manager Thomas Tuchel’s squad over the international break.
"I would say to him Phil Jagielka, Leighton Baines, Joleon Lescott - that's three who we brought in and went on to become international players for England, which was a great achievement.
"I think Jarrad is in a position where he could easily go on and do that. I see it as a challenge for Jarrad to pick up and say 'come on, I'm going to show what I can do'.
"This club has developed quite a few England internationals over the years. We've got a very good goalkeeper who is playing for England as well."
Finally, Moyes says the players should be the ones who are praised for turning the club around since he arrived as manager and not him.
"It (the stats) says that the club and certainly the team are on a better trajectory than we were before. We've started really well. The players have done a brilliant job.
"There is a lot that can be said about a new manager coming in and I know it is our job to get them playing, but I have to say that the players have picked themselves right up, they have turned the whole place around - the crowd and the support - and they have gone on a run, which has been really good.
"Actually, we were a bit disappointed with a couple of the draws in there, that we didn't get victories.
"There might have been a couple of draws in there which we could have been a bit lucky with but, overall, I think the players have got everything they have deserved.
"They have got the results and we want to keep it going."