The Old Trafford club have turned down a second approach from Chelsea for the striker, who was not involved in the 1-1 friendly draw with AIK due to a shoulder injury
The Premier League champions confirmed they had rejected a second bid from the Stamford Bridge outfit, who have made the England international their priority transfer target this summer.
But Moyes does not expect the 27-year-old to force his way out of Old Trafford due to the club's illustrious standing in football.
"I don't know, I've not asked him," said Moyes when asked what Rooney had made of Chelsea's second bid being rejected.
"Will I try and persuade him to stay at the club? You don't need to convince anybody to stay at Manchester United."
Rooney was not involved in the 1-1 draw with AIK due to an injury, but Moyes insisted the striker's shoulder complaint was genuine.
"I don't think it will keep him out very long. He fell on it the other day [against Real Betis]."
The Scot offered no update on the club's pursuit of Cesc Fabregas, but expects signings to be made this summer.
"I can't say anything [about Fabregas]," Moyes said. "But there will [be signings] and they will come."