The Black Cats are yet to sign a player this summer but Moyes says moves have already been made behind the scenes.
The former Everton and Manchester United manager was confirmed as the new Black Cats boss last month after Sam Allardyce became the new England coach.
Fans are keen to see him get to work in the transfer window, with no new signings having arrived at the club so far.
Indeed, Allardyce had openly discussed his frustration about the lack of movement before he departed the club.
Moyes has moved to ease their fears though, saying that they already have offers in for players.
“We have offers in for people already and we’re working hard. I’ve been really impressed by the new chief executive,” he told the Chronicle.
“This has to be a building job. I’m here for four years and I’m aiming to bring stability. Sunderland have potential that many clubs don’t have, but we have to progress.”
It now remains to be seen what players Moyes can bring in before the end of the transfer window.
The Black Cats squad does need improving if they are to avoid another relegation battle and become the stable club that Moyes wants.
Chief among his targets is likely to be another striker, especially with Jermain Defoe picking up a thigh injury in pre-season and facing a fight to be ready for the start of the season.