Real president Ramon Calderon has revealed the club "are now going to make an effort" to keep the England midfielder at the Bernabeu despite him having signed a big-money deal with the Galaxy which will start on July 1.
Reports in the Spanish media claim there is a clause in the England midfielder's Galaxy contract which gives them an option to keep him.
But Beckham's spokesman said: "There is no intention of getting out of the Galaxy contract.
"David is looking forward to going to LA - but he wants to end his career at Real Madrid on a high note first, by winning the league."
Calderon had told Spanish newspaper Marca: "We need to sit down with him, his representatives and with (Real sporting director Predrag) Mijatovic, look at this clause, and decide between us, but for me I would be delighted if he remained at the club.
"There was a bit of anger by the premature announcement of his exit, but we are now going to make an effort for him to stay."
Beckham was told he had played his last game for Madrid by coach Fabio Capello when he agreed to join the Major League Soccer side in January but he has been instrumental in their late title charge, with a victory over Real Mallorca all that stands between them and the Primera Liga crown.
The midfielder, who suffered an ankle injury on duty for England against Estonia, played through the pain barrier in Saturday's 2-2 draw with Real Zaragoza and Calderon paid tribute to the former Manchester United midfielder's courage and spoke of his desire for him to remain with the club.
"Beckham has shown that he is a great player, with great pride," he added.
"He is playing at a great level and on Saturday he fought even though he was half-injured against Zaragoza.
"The Madrid supporters love him, and for me I would like him to remain in the team."
Capello revealed last month Beckham's attitude and form had left him with no option but to go back on his word and restore him to the side and led the calls to end his international exile.
"I believe that he has never been in better form in the last two years than he is now, and he agreed with me," said Capello.
"I have told him that I cannot understand how someone playing so well can be left out of his national team."
Steve McClaren duly agreed and Beckham did not disappoint, starring on his return to the international fold.
First he delivered a trademark cross for the man who succeeded him as captain, John Terry, in the friendly against Brazil on June 1 before two more assists in the 3-0 victory in the Euro 2008 qualifier against Estonia last week.