Moyes has poured cold water on suggestions he went on a scouting mission over the weekend, when he was spotted watching matches involving Juventus and Paris St Germain.
Even the departure of Brazil midfielder Anderson on loan to Fiorentina has been compensated for by the long-awaited return to fitness of Darren Fletcher.
Yet, given the lack of high quality options in his present squad, which have been brutally exposed at times this season, it would be a major surprise if Moyes was not plotting something.
And the Scot confirmed work was under way, even if it might not bear fruit.
"We are looking really hard," he said.
"As I have said many times, it is not a particularly good month to buy players.
"I would hate to get people's hopes up and end up with nobody.
"In the same breath we are certainly not sitting back and doing nothing, that's for sure. If we could pick up one or two players in this window we said we would try and do it."
Having failed with one attempt to sign Fabio Coentrao from Real Madrid, Moyes will have noted with interest the Spanish giants being linked with Sevilla's Alberto Moreno.
Benfica defender Ezequiel Garay, who has been linked with a move to United on numerous occasions in the past, is also being bandied about as a potential January signing.
Midfield is an obvious area of weakness, so much so that it has been suggested Moyes would be willing to spend big to lure Paul Pogba back to the club, despite the fact Sir Alex Ferguson let the France international leave for nothing in the summer of 2012.
"I can see it is a big task and a big job to get things the way I want it," said Moyes.
"Everybody recognises we have to make some changes. But that is not the reason for me globe-trotting all the time.
"I have always been an avid football watcher. I have always enjoyed going to games.
"When you are at a club like this, attention gets drawn to the fact you are there, then people make assumptions that you must be watching one player or another.
"But you don't always sign a player when you go to a game. In fact, you probably go to very few and do that.
"Maybe we are looking for the summer, not for now.
"The point is when you are at Manchester United you are in the spotlight wherever you go."
However, it is a fact that Anderson's time at the club is drawing to a close.
The 25-year-old, who joined United from Porto in 2007, has agreed to join Fiorentina on loan until the end of the season, by which time he will have a single season remaining on the contract he extended in 2010.
Given his lack of recent appearances, the Brazilian, who took a penalty in the Champions League shoot-out triumph over Chelsea in Moscow, has not convinced Moyes of his quality and it is not expected he will play for United again.
"We've not been able to get him as many games as he hoped, so we feel it is a good opportunity for him," Moyes said.
"He's going to a good club in a good league, so hopefully it gets him some benefit."