The Scot will take charge of his new side for five games in Asia and a further game in Europe from July 13, before his first game at Old Trafford in a testimonial match for Rio Ferdinand.
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"I'll try [to bring some players in before the tour] but I couldn't honestly say yes. I will try if possible. Time is closing in a little bit just now," Moyes told reporters.
"The way the transfer window is, I think things might be done a little bit later in some cases this year. Partly because there are quite a few new managers in, as well, I don't think everybody will be done right away. In the ideal position we'd get players in right away."
The Scot refused to comment on speculation regarding other clubs' players although confirmed that United would always be in the market for top talent.
"We will do everything we can to add to the squad. This club is always interested in the best players," he continued. "This club has done it. We'll do everything we can to make sure we remain at the top.
"I would never speak about players at other football clubs – I think it's wrong, it's not my style. I'll answer as many questions as I can but, when people have a contract at other football clubs, I think it's wrong to talk about them."