Rooney's future at Old Trafford has been shrouded in doubt throughout the close-season, with Chelsea already having a bid for the England international rejected.
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The 27-year-old has been unsettled since being left out of the United team to play Real Madrid in the second leg of their last-16 Champions League tie in March by former manager Sir Alex Ferguson.
Rooney has also flown home from the club's pre-season tour of Asia with a hamstring injury, but after watching his side lose to Yokohama F. Marinos on Tuesday, new boss Moyes revealed the striker should be available for their friendly with AIK on August 6.
"I do expect Wayne to be in Stockholm," the Scot told reporters.
"As far as I know he is coming on, he has started light jogging and the feedback from the physios is that he is progressing so hopefully those dates will still be right when we get back."
With Chelsea rumoured to be preparing another bid to take Rooney to Stamford Bridge, Moyes also reiterated that the player will not be sold.
"We have said and the club have said he is not for sale," he insisted. "That has not changed."