Moyes targets more success with Maguire and Ward-Prowse deals close
Reports in British media this week said West Ham had agreed deals worth around £30 million each for both England internationals.
Asked about the signings, Moyes told reporters: "We're not denying it, James Ward-Prowse is having a medical with us now.
"I don't know if it's right to talk about players when we've not actually signed them yet, but yes, we've agreed a fee...," added the English manager, speaking ahead of Saturday's season-opening trip to Bournemouth.
"We've also had a bid accepted from Manchester United, but while he's not our player I'm not in position to discuss him, really."
Moyes also revealed that West Ham had received a bid from Manchester City for Brazilian international Lucas Paqueta, but added that the offer was"not anywhere near meeting our valuation".
West Ham won the Europa Conference League and secured a 14th-place finish in the Premier League last season, with their European success earning them a place in the Europa League.
Moyes said the club are hoping to once again be competitive both domestically and in Europe, saying: "We played 65 games the season before last and 61 last season, which was incredible...
"That's mainly down to our success and we want to build on that. We want to start well, but it's where you finish that's important. We didn't finish last season in the league where we wanted to be, but also we didn't finish where we didn't want to be."