There are no guarantees of success and it is thought a deal remains highly unlikely before the Chinese transfer window closes on 28 February.
But the fact Stretford has travelled to China is a clear indication United boss Jose Mourinho would let Rooney, 31, go.
Rooney has fallen down the pecking order at United under Mourinho.
The England captain has been made aware of interest in him from the Chinese Super League for some time, although it is not known which clubs Stretford has spoken to.
However, two of the three clubs who looked the most likely options for Rooney have ruled themselves out.
Beijing Guoan, believed to be the favourite team of Chinese President Xi, had been seen as one of the favourites to sign Rooney but sources close to the club have told BBC Sport they are not interested in signing him.
The England captain’s representatives have already spoken to Tianjin Quanjian and their coach, Fabio Cannavaro, said talks did not progress, while sources close to Jiangsu Suning also dismissed speculation over a transfer.
On Tuesday, Mourinho said he did not know whether Rooney, who has only just returned to training after a hamstring injury, would still be at Old Trafford in a week’s time.
It is not known whether this latest development will affect Rooney’s chances of being involved in Sunday’s EFL Cup final against Southampton.
They had appeared to have increased after Henrikh Mkhitaryan limped out of Wednesday’s 1-0 Europa League win against Saint-Etienne.
If Rooney follows former team-mate Carlos Tevez to the Chinese Super League, it would almost certainly cost him any chance of making the seven appearances he needs to become England’s most capped player.
Rooney’s preference is understood to be to remain with United for the rest of his contract, which expires in 2019, but a lack of time on the pitch is forcing him to consider alternatives.
Rooney is United’s record goalscorer and has won five Premier League titles and a Champions League trophy since joining them as an 18-year-old for £27m from Everton in 2004.
The forward, who has started only three games since 17 December, has said he would not play for an English club other than United or Everton
The big difference between Chinese Super League clubs’ transfer process and their Premier League counterparts is the preparation.
English top-flight clubs have extensive scouting departments with links around the world. They identify players months in advance, watch many live games and base their decision on an extensive process.
Oscar moved to Shanghai SIPG from Chelsea in a £60m deal in December and scored on his debut for his new club
In CSL, the process is more agent-led. Most of the clubs are approached with recommendations for a position they are recruiting in, rather than seeking out players themselves.
Foreign players coming in on large fees are commanding three-, four-, five-year deals, even at the end of their career. They have the upper hand in negotiations and wouldn’t leave European football without long-term financial guarantees.
However, the Chinese government is concerned about capital leaving the country and it is difficult for these big transactions to exist while they are trying to crack down in other areas.
I think we will see a levelling out in fees. The £15m-£20m transfers will continue to happen for the next few years, but maybe we won’t see the likes of the £60m deal that brought Oscar to China.
Credit: BBC NEWS