The champions begin the defence of the title with a tricky trip to Wales to take on last year's Capital One Cup winners, who have invested heavily in the squad during the close season and breezed past Malmo in the Europa League qualifiers.
In an exclusive interview with Countdown to Kick-Off on MUTV, the manager outlined how he expects the Swans to provide a stern test but is pleased with the way that things are shaping up ahead of the tea-time kick-off in terms of his own team plans.
"It's a very tough away fixture," explained Moyes to MUTV. "Michael Laudrup has done a really good job there and strengthened the team a lot this summer. I would expect Swansea to have another season as good as last year and they've already had a couple of European games as well which gives them the feeling they are a little more match-ready.
"We know it will be a hard game but we feel we're getting ready as well and getting everybody back fit. Because of that, hopefully we'll go there and give ourselves a good chance of winning. The only real injury we've had is Rafael's that looks like keeping him out for four-to-six weeks with a hamstring. We've had a few other small niggles, keeping people out for a few days, but, hopefully, most people will be available and ready for the game."
Leading United into league combat for the first time, after winning the Community Shield last weekend, is clearly something that excites the new manager.
"Everybody wants to play Manchester United and do well," he stated. "I'm sure I'm going to be made aware of that very early.