The Sun says the Spanish giants contacted LA Galaxy last week - and were promptly turned down.
Real even told Galaxy to name their price - but they were having none of it. The Americans also laughed off a proposal to loan Beckham, 32, back to Madrid for up to two years.
It is an embarrassing state of affairs for Real who, inspired by Beckham, will win the Spanish La Liga title next Sunday if they beat Real Mallorca.
And president Ramon Calderon yesterday tried to calm fans angry at Beckham's departure.
He said: "Beckham has shown he is a great player with great pride.
"The Madrid fans love him and I would like him to stay in the team.
"In the contract he signed with LA Galaxy, there is a clause allowing the player to back out.
"We have to look at this clause and decide between all of us but I would love him to remain at the club."