Rooney missed United's entire pre-season programme with hamstring and shoulder problems amid claims he had been frozen out by Moyes after telling him he wanted to join Chelsea.
United have turned down two Chelsea offers for Rooney and Moyes is adamant the England striker is not for sale, although Blues boss Jose Mourinho has made it clear he still hopes to sign the 27-year-old before the transfer window closes.
Moyes was at Wembley on Wednesday to see Rooney finally prove his fitness by playing 66 minutes of England's 3-2 friendly win over Scotland and the forward travelled with the United squad when they flew to Swansea on Friday afternoon.
However, with last season's star man Robin van Persie netting twice in Sunday's Community Shield win over Wigan, Moyes could be willing to risk angering the notoriously short-tempered Rooney by leaving him on the bench at the Liberty Stadium, where the champions will play a league game with a manager other than Alex Ferguson in the dug-out for the first time since November 1, 1986.
"Everybody wants to play Manchester United and do well," Moyes said of the test Swansea will pose.
"I'm sure I'm going to be made aware of that very early. But to be called Manchester United manager is probably the biggest thrill.
"It's a real privilege and I'm going to do everything I possibly can to make sure the club continues to have success."
United's two closest rivals from last season are also under new management, with Manuel Pellegrini replacing the sacked Roberto Mancini at Manchester City and Mourinho returning to Chelsea to succeed Rafael Benitez.
City, who have spent an estimated £90 million ($139 million, 105 million euros) on new players, do not begin their season until Monday, when they host Newcastle United, with Chelsea in action a day earlier when promoted Hull City are the visitors to Stamford Bridge.
Sunday will also witness another encounter between a promoted club and a budding title contender, with Tottenham Hotspur travelling from north to south London to take on Crystal Palace.
Like City, Spurs have also spent heavily in the close season, with Thursday's acquisition of France midfielder Etienne Capoue from Toulouse nudging their total outlay towards the £60 million mark.
It is Gareth Bale's mooted move to Real Madrid that has most occupied manager Andre Villas-Boas' thoughts this summer, however, although the Welshman will be absent at Selhurst Park with a foot injury.
Once again, Spurs begin the season with the aim of pipping north London rivals Arsenal to a Champions League spot, having narrowly failed to meet that objective last season.
Arsenal are yet to add any new players to their squad, to the consternation of their fans, and manager Arsene Wenger also has injury concerns in midfield ahead of Saturday's visit of Aston Villa.
Santi Cazorla may be short of fitness after turning out for Spain against Ecuador, while Mikel Arteta is sidelined with a thigh problem and Thomas Vermaelen has a stress fracture in his back.
"I understand everyone's frustration, but what is important is the quality of what you do on the pitch, so let's not create a crisis from nothing," Wenger said.
"The first request (for new signings) is to have the quality to play for Arsenal."
The new season kicks off at Anfield, where Liverpool come up against a Stoke City side with a new manager in Mark Hughes.
With unsettled striker Luis Suarez absent as he continues his 10-game ban for biting Chelsea's Branislav Ivanovic last season, Liverpool manager Brendan Rodgers has been boosted by the news that Daniel Sturridge has overcome an ankle problem.
Former Wigan Athletic manager Roberto Martinez takes his new club Everton to Norwich City on Saturday, while Cardiff City, promoted as winners of the second-tier Championship, visit West Ham United for their first top-level match since 1962.
Paolo Di Canio's Sunderland, and their 10 new signings, begin the campaign at home to Fulham, while Southampton will have club-record ?12.5 million signing Victor Wanyama on board for their trip to West Bromwich Albion.
Opening Premier League fixtures
Saturday (1400GMT unless otherwise stated):
Liverpool v Stoke City (1145GMT), Arsenal v Aston Villa, Norwich City v Everton, Sunderland v Fulham, West Bromwich Albion v Southampton, West Ham United v Cardiff City, Swansea City v Manchester United (1630MT)
Crystal Palace v Tottenham Hotspur (1230GMT), Chelsea v Hull City (1500GMT)
Manchester City v Newcastle United