The Holland international played a key role in the Spainards' successful defence of their La Liga title last season after joining from Ajax, but he is set to miss six months after damaging knee ligaments against Arsenal in the Emirates Cup on Sunday.
Real have been trying to land United winger Ronaldo all summer and their need for a playmaker has now intensified.
Real Madrid president Ramon Calderon said: "We are very upset about Sneijder's injury. It's serious and it's the worst news we could have.
"He is very bad, very upset. He is crying because it is a very serious problem and very painful."
Ronaldo could cost Real in the region of £70m but they would have to wait for him to return to full fitness after post-Euro 2008 ankle surgery.
Sir Alex Ferguson will now be braced for a massive bid and will know he has to pull out all the stops to keep the 23-year-old at Old Trafford.
Man United last week