The 19-year-old visited United's training ground on Friday as United try to tie up a deal with the player.
The Dutch Young Player of the Year has attracted the interest of a host of top clubs but United are favourites to land the striker.
Ferguson is keen to bolster his attack and has been linked with a number of strikers including Louis Saha, Mark Viduka and Jermain Defoe.
"We are interested in him," Ferguson told the Mail on Sunday
"Nothing's been finalised but we are hoping to do business with PSV."
Real Madrid have also been linked with Robben, but the player's father and agent Hans Robben has ruled out a move to Spain.
"Money is not a big issue for our family," said Robben. "We are down to earth people and Arjen will never ever have flash lifestyle. We don't need agents and Arjen is a happy quiet, happy lad.
"Real Madrid also want him but he won't go to Real. What is the point?
"It is not the place for a young boy like my son. And he never liked Real anyway. When we were in Spain, he only liked Barcelona.
Robben, who is ineligible for the Champions League having featured for PSV this season, is likely to agree a deal with United for next summer which could see him loaned back to PSV.
Meanwhile, Ferguson had revealed he is close to signing his new deal at Old Traford.
Ferguson has been locked in talks over an extension that would keep him at the club until 2007 for several weeks and he is now ready to put pen-to-paper.
"There are no problems whatsoever," said Ferguson. "The club are happy with the terms and so am I."