Robben took advantage of the winter break in Holland to fly to England and have talks with United, with a view to joining the Premiership club.
The player's father recently insisted that there had been no concrete offer from United, but it appears that Sir Alex Ferguson has stepped up the chase for the 19-year-old.
Ferguson has hinted that another striker is his main transfer priority, although Robben would not be available for UEFA Champions League games having played in the competition for his Dutch club.
PSV have already confirmed that a top European club are in for their young star, who was the Dutch Young Player of the Year last season.
Meanwhile, Red Devils starlet Cristiano Ronaldo has been allowed to fly back to Portugal for a holiday.
"We were always going to give him a holiday," said Ferguson.
"It was just a matter of deciding when."