United have had a couple of bids for Barcelona midfielder Cesc Fabregas rejected this summer, but Moyes is expecting some new arrivals at Old Trafford in the near future.
Speaking at the launch of the new Premier League season, the Scot told Sky Sports News: "I'm confident we will have players in.
"We are involved in several players we are looking at and that will continue. Will we get them before the deadline? I hope so, but we are working very hard to do so."
Moyes admits it has been a busy summer for him after taking over the reins from Sir Alex Ferguson.
He added: "This was always going to be a difficult window for me personally because I joined Manchester United on 1 July so it is giving you a short period to get to know the players and to get to know the market.
"Yes of course I was working on it during the summer but it is never the same until you have actually worked with the players and been around them.
"But what I do know is the group of players we have got are a great group of players - they won the Premier League last year.
"We have got lots of young exciting players - a lot of them played for England last night - so it is important that we focus on the players we have got at Manchester United and how well they have done last year.
"There is not much change so hopefully they will be able to continue the way they finished last season."
Ferguson is now a director of the club and Moyes says he has spoken to him regularly during the off-season.
He added: "I went to see him at his house and I speak to him quite regularly on the phone. It's good to have someone I can go to if I need any advice, especially at a club like Manchester United.
"He's great and he's someone I look forward to taking advice from in the future."