Moyes has been frustrated by the club's lack of signings and he made it clear he wanted reinforcements after the Carabao Cup second-round win against Preston on Wednesday.
The Toffees have been searching for a replacement for right-back Seamus Coleman for more than a year.
Moyes stressed any decision about Armstrong's future would ultimately rest with Everton, owned by The Friedkin Group.
"It's not really a question for just now. It will be a club decision," he said.
Speaking to Sky Sports, the Scot also questioned whether the summer transfer window should remain open once the season has started.
"For all the years I've been in the Premier League this is probably the first time I've thought it was really a nonsense we're still playing games when the window is still open," said Moyes, who is in the final year of his Everton contract.
"It feels like we'd have been better off just getting it shut.
"Maybe it's just the way I am at the moment, I might feel better on Tuesday, but just at the moment it just leaves too much open, too much talk, mainly from the media.
"If I look back over the years, back to Wayne Rooney, Mikel Arteta, Joleon Lescott, players at Everton I didn't want to lose, more recently Declan Rice at West Ham, sometimes it's part of the journey and you have to rebuild."
The window for the Premier League and EFL clubs to make new signings is to close on Tuesday, 1 September at 23:00 BST.