Having succeeded Sir Alex Ferguson at Old Trafford, Moyes has been released from the transfer shackles which occasionally left him frustrated at Everton.
There is no bottomless pit of cash at United, but the Scot claims to have been informed that there are no budget constraints.
That has given him the freedom to chase any target he likes, with United reported to still be mulling over approaches for Tottenham Hotspur forward Gareth Bale and former fans' favourite Cristiano Ronaldo - who remains on the books at Real Madrid.
Moyes is reluctant to divulge the identity of those on his summer shopping list, but expects to be backed by his board in any decisions he takes.
After seeing his first game at the United helm end in a 1-0 defeat to the Singha All Star XI on Saturday, Moyes said: "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'.
"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.
"I will not name anybody, but certainly we are always looking at the best players. 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."