United have lost three of their first six Premier League games since Moyes succeeded Alex Ferguson, which represents their worst start to a season in 24 years.
Moyes missed out on a number of transfer targets during the close season, including Everton left-back Leighton Baines and Athletic Bilbao midfielder Ander Herrera, but he says fans should not expect a flurry of activity when the transfer window re-opens.
“I’ll look at January, but I wouldn’t want people to have big expectations of what we would sign or do,” Moyes said, ahead of his side’s trip to Sunderland on Saturday.
“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.”
However, Moyes did admit that the club were on the look-out for players capable of improving the champions’ squad.
“Undoubtedly we will, in time, try and make the squad better. The job is to make progress at Manchester United,” he said.
“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 affect on the first team.”