United have been unsuccessful in their pursuit of Barcelona midfielder Cesc Fabregas, and appear unlikely to get the player.
Moyes is apparently interested in Everton duo Leighton Baines and Maroune Fellaini, although he has still to approach his former club regarding the duo.
And while Wayne Rooney is unsettled, he remains at Old Trafford, meaning only Paul Scholes has left the club this summer.
Moyes, preparing his team for Monday night's friendly against Kitchee FC in Hong Kong, insists he has great faith in the pool of players that strolled to the title last season.
"This is the squad that finished 11 points clear at the top of the league last season so I am confident in the squad," he said.
"But even without additions this squad will be tough opponents for any team - they will be looking at Manchester United.
"We know we will be challenged by everybody, every game we play."