The Reds strengthened in the summer with the acquisition of Marouane Fellaini from Everton on deadline day and speculation has been rife ever since the window closed that others could follow the Belgian into Old Trafford next year.
As Moyes is impressed with the depth of the squad already at his disposal, he only feels one or two new faces are required to enhance the side.
"Look, the quality of the players here is really top-end," he stated. "They are great players to work with but, undoubtedly, we will, in time, try and make that better - the job is to make progress at Manchester United.
"They won the league last year but I want to try and progress on that, try to win it again and try to win the cups if possible as well. We'll also look to add to the squad if the right players become available."
When quizzed specifically on the prospect of entering the market in the New Year, the boss was happy to outline his current thoughts on the subject.
"I think I'll look at January but I wouldn't want people to have big expectations of what we would sign or do in January," he replied. "Because I don't think January has, in the main, been a great month to sign really at the top [level].
"I think if you're in trouble near the bottom you might [sign players] as you're desperate for something. But where I think we will be with Manchester United is looking for [only] the top players."