Top of the agenda for the large group of assembled journalists was Cristiano Ronaldo, who has been consistently linked with a return to Old Trafford from Real Madrid.
Moyes refused to be drawn on the Portuguese star but says the Reds will "do everything we can to add to the squad".
"I would never speak about players at other football clubs," the former Everton boss said. "I think that’s wrong and that's not my style. I’ll try and answer as many questions as I can but when people have contracts at other football clubs I think it's wrong to talk about them. But this club is always interested in the best players.
"Manchester United had a great season in the Premier League last year and we'll do everything we can to add to the squad. This club will always go after the best players and we'll do what we can to remain at the top.”
When asked if he would bring in new players before the start of the pre-season tour next week, Moyes added: "I'll try but I couldn't honestly say yes. Time is closing in a little bit just now.
"I think the deals may be done a little later this season. There are a few new managers so I don't think everything will be done right away."
At various points in the press conference, Moyes emphasised his strong desire to continue the traditions of the club – not least bringing through young talent.
"Everton don’t shop in the same window Manchester United shop in," he added. "But this