The defender suffered a shoulder injury during Tuesday’s win over Hull City, while the striker is likely to miss Sunday’s fixture against Southampton with a groin problem
Jones suffered a shoulder injury during United's 3-1 win over Hull City at Old Trafford on Tuesday, while Rooney has missed the club's last two matches with a groin problem and is a doubt for Sunday's final game of the season at Southampton.
"Phil's injury isn't as bad as I thought on the night. He's obviously out for Sunday but should be OK for the World Cup," the 40-year-old told reporters.
Giggs revealed that Rooney has taken part in training this week but admits that the game against Mauricio Pochettino's men may come "too quick for him".
England's 23-man World Cup squad, plus an additional seven players on standby, will be named by Roy Hodgson on Monday before the squad fly to Portugal for a training camp.
England will return to face Peru at Wembley on May 30 and will then travel to Miami where they will play warm-up games against Ecuador and Honduras.
Hodgson's men face Italy in their Group D opener on June 14.