Express Sport understands it is unlikely United's record goalscorer and captain will leave for the Far East this month.
The transfer window for the Chinese Super League shuts on Tuesday.
But Rooney's representative is apparently listening to offers as the 31-year-old seeks a world-record salary.
According to The Sun, Stretford is negotiating with teams in China who are willing to offer Rooney £1million a week.
Wayne Rooney is unlikely to move to China this month but his agent is holding talks
The agent is said to have flown to China a few days ago and spent time in Tianjin.
Tianjin Quanjian are one of the clubs to have made an approach for Rooney, while talks with other suitors are being held too.
One side has tabled a contract worth £650,000 a week after tax, which runs for three years.
And that proposal would also see Rooney paid six months of his salary up front, as well as a signing-on fee, which equates to £25m.
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Who could replace Wayne Rooney if he left Manchester United
He’s not agitating for a move but, if the right offer comes in, something is likely to happen
Man Utd source
A source told The Sun: “Wayne has generally been very happy at United for the past 13 years and was delighted to become the club’s record goalscorer.
“But he has dropped down the pecking order and there comes a time in everyone’s career when you have to consider whether it might be sensible to move. He’s not agitating for a move but, if the right offer comes in, something is likely to happen.
“It’s highly unlikely a move will be completed before the end of the Chinese Super League transfer window though.”
Chinese president Xi Jinping would apparently need to sanction any record-breaking transfer.
And while Rooney is not being pushed out the door by Jose Mourinho, the United boss couldn't guarantee this week that the forward would be at Old Trafford by the summer.