The Red Devils have endured a difficult start to their Premier League title defence after losing three games in six top-flight outings.
United failed to land a big-name in the summer transfer window as Moyes was thwarted in his pursuit of Barcelona midfielder Cesc Fàbregas and Thiago Alcantara.
The Red Devils did sign Marouane Fellaini in a £27.5m deal from Everton on deadline day, and Moyes believes United only need one or two shrewd additions to strengthen their current squad.
“I’ll look at January but I wouldn’t want people to have big expectations of what we would sign or do,” Moyes said. “In the main, January has not been a great month to sign at the top level.
“If you’re in trouble near the bottom you might as you’re desperate for something but we’ll be looking for the top players.
“Undoubtedly we will, in time, try and make the squad 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.
“We wanted to try and get one or two players in which, I said at the time, we wanted to buy players to come into the team if possible.
“That was the goal. We didn’t need many more players, just one or two who could definitely help and effect on the first team.”
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