The midfielder has shone since joining the Rams on-loan in January.
Asked if Armstrong is ready to walk into the Everton first team next season, Moyes said: "Walk into the first team is a big statement (But) be part of the squad and be around it is probably something which is more likely. So, that's where the decision comes – is he young enough where he needs more games yet, so he can get more experience before coming in?
"I'll assess that in pre-season. I'll bring him back in, hopefully he'll get some playing time in the games in pre-season and we'll see how he does – and decide then if we think he needs another loan, or if we need to keep him.
"But we like him. It's not as if we're going to sell him or anything like that – we like him and we want him around but, again, we might look at it and think about him getting another 30-40 games. To get a young player games in the Championship is not as easy as you think because it's a tough league and it's credit to him that he's gone in there and got himself a steady position."
Contract talks planned
Moyes also admitted they face major work in the coming weeks regarding player contracts, with many senior players' deals running down.
He added, "We've got a few, as you all know, who are coming out of contract. We're still in a situation where we want to keep everybody right.
"We'll not wait until the last minute to do it but we will certainly do it when we're ready and it won't be dictated by the players – they are under contract at the moment and the Club will decide at the right time when to make decisions on the players.
"The players can influence things on the pitch – that's their job, isn't it? Their job is to make it easy for the decision to go in their favour, obviously."