Reports emerged on Thursday suggesting the England international had left training prematurely to undergo a scan on a groin injury, sparking immediate fears over his involvement for Roy Hodgson's side at the global showpiece in Brazil that starts next month.
Speaking at his pre-match press conference ahead of United's Premier League game with Sunderland on Saturday, Giggs revealed that Rooney had a slight groin strain and was also struggling with illness.
However, the striker has not yet been ruled out of facing Sunderland at Old Trafford.
"A few of the lads have had a bug. Anders Lindegaard has, Wayne Rooney has too. Wayne also has a tight groin," said Giggs.
"You have to be careful with the bug because the immune system is down a bit but, Wayne being Wayne, he wants to play. We'll monitor it over the next 24 hours."
Giggs was handed a further boost this week with Robin van Persie's return to training following a six-week lay-off with a knee injury, although Saturday's game may come too soon for the Dutchman.
"Robin has been back training this week. He's looked good," Giggs added.
"Whether tomorrow is too early we'll just see how he goes today. He's looked really good this week."
Giggs will lead United for the second time since being asked to temporarily take the reins after the dismissal of David Moyes.
The Welshman is looking for back-to-back victories following last weekend's 4-0 rout of lowly Norwich City.
