The Colombian ace is currently on loan at Old Trafford from Monaco, and has already been linked with a permanent switch at the end of the season.
But after being interested all over the summer, Real have also been linked with a rival swoop for the prolific marksman.
However reports now suggest that the Spanish giants are reluctant to sanction a big money raid given the 28-year-old’s injury concerns.
Falcao ahs only recently returned from a serious knee problem sustained while at Monaco, which ruled him out of the World Cup.
United are also believed to be concerned by the South American, who has only managed three starts since joining the club – netting one goal in the process.
Reports suggest a clause to keep him is in place, but Louis van Gaal’s side will have to pay around £50m in order to do so.