Rooney has been peripheral to Jose Mourinho's plans at Old Trafford and it seems that his future appears to be heading towards a move away from United.
The club captain and all-time leading goalscorer is no longer an automatic starter and was an unused substitute in last month's EFL Cup final victory over Southampton.
His circumstances have sparked speculation of a move to China, where Eriksson is in charge of second division side Shenzhen FC.
Eriksson has previously talked up a future move to the region for Rooney, however, the 69-year-old believes the veteran has more years left in him at the elite level.
"I would be surprised if he wasn't in the United or the England team for the next years," he told Omnisport . "I'm quite sure he will be."
"He is a proud man. He is a skilful man and he is a man that can play many different positions.
"I hope to see Rooney on the biggest stage for many years still. One day he might end up in China."
Meanwhile, the Swede says he could have bet on Zlatan Ibrahimovic being successful at Manchester United.
There were doubts whether Ibrahimovic could cope with the demands of the Premier League, but the Swede has continued to defy his age and critics in England with 26 goals in all competitions.
The 35-year-old has scored 15 of those in the top flight but is yet to sign a contract extension, having agreed a one-year deal with the option of a second when he joined on a free transfer in July.
But despite Ibrahimovic turning 36 in October, former England and Manchester City boss Eriksson thinks his compatriot's stay at Old Trafford should be extended.
"If he takes a challenge like Manchester United, I could've bet that he would be successful," Eriksson said.
"He wouldn't have done it otherwise. If he feels his body couldn't do it, he wouldn't go because he is extremely proud and he is training very hard. He is very fit.
"The day he can't do it anymore, he will be the first to say stop because he doesn't want to be a failure and he won't be.
"He is a great player. He can play in any team in the world. The only pity is that he doesn't play for Sweden anymore.
"I would give him a new contract if he told me he could do it."