The Brazilian, who only joined the Premier League strugglers during the summer, has been in fine form this season, helping to keep the Londoners within touching distance of safety.
But, they now face a fight to keep him at Loftus Road, with Real lining him up as a replacement for Iker Casillas.
The Spaniard has been ruled out for up to two months through injury, leaving manager Jose Mourinho short of goalkeeping options.
‘The Special One’ coached Cesar during his spell with Inter Milan and is now keen to bring the stopper to the Bernabeu to solve his current selection headache.
Super Hoops boss Harry Redknapp is believed to be willing to let one of his two goalkeepers, the other being Rob Green, leave this winter as he looks to reduce the club’s spiralling wage bill.
Cesar, who earns an estimated £70,000-per-week, may be convinced to move on, with Real providing him with another chance to compete at the very highest level.
Officials from the Galcticos have reportedly made contact with the 33-year-old, but there has been no concrete bid made.
Meanwhile, QPR are preparing a fresh bid for West Brom striker Peter Odemwingie, believed to be in the region of £3m.