The Premier League champions were widely expected to make some big signings in Moyes's first transfer window in charge, but so far only young Uruguayan full-back Guillermo Varela has arrived at the club.
There have been embarrassing rejections from Barcelona and Everton, with the former's Cesc Fabregas revealing he never wanted to leave the club, and the latter's management calling a £28 million double-offer for Marouane Fellaini and Leighton Baines "insulting".
The Reds have conducted their business relatively publicly by their standards, leading some to question their seriousness about making major changes to a squad which won the title.
Moyes said that, while on the lookout for players, he is prepared for a fruitless summer.
"There is no pressure to (make signings). I have an idea of where I'd like to strengthen but we won't do it because people tell us we should be signing players," he said.
"If the right players are available, then great, but there is a possibility nothing may happen.
"(If not) the first thing we'll do is encourage our own young players in the squad to do as well as they did last year."
That will infuriate some supporters, who have seen the likes of Manchester City, Chelsea, Tottenham and even Norwich and Southampton add major international players to their squads.
However, United have been linked with a second offer for Everton's Fellaini and Baines, while Real Madrid's Mesut Ozil and Southampton's Luke Shaw have been identified as possible targets.