The former Everton boss was named Sir Alex Ferguson’s successor in May and a host of big names have since been linked with moves to Old Trafford.
After seeing his first game at the United helm end in a 1-0 defeat to the Singha All-Stars in Thailand on Saturday, Moyes revealed he is looking to bring in some new faces.
"Isn't it great that the club says, 'There's no budget here, you go get who you want to get, just go and do it'," he told reporters.
"We are looking at the best players. I do think it's important that we show people we are carrying on the traditions and trying to take the club forward."
|MOYES TIGHT-LIPPED ON RONALDO
|9/4||Manchester United are 9/4 with bet365 to win the Premier League
"I will not name anybody, but certainly we are always looking at the best players," he added. "I think we are trying to strengthen in a couple of areas. We are short in midfield.
"We are also a club which tends to invest in the youth side, so you can expect us to go for players in that age group.
"We are working hard to make sure the first signing is the right one. I have been left a really good team and I want to add to it sensibly."
The 50-year-old also admitted that while taking over the Old Trafford reins from Sir Alex is no easy task, he sees no reason why the club should alter their targets for the season.
"Our objectives for the season ahead are no different from what any Manchester United objectives would be - to win as many trophies as possible," the Scot continued.
"It's my first season as manager of Manchester United. I'm following probably the finest football manager that's ever lived. If I could even win a quarter of what he won I've done very well.
"The first thing I've got to do is settle in to the job, get to know everybody and find my own way around. Everyone at the club has been making that as easier as possible for me, the players especially have been terrific."