Madrid agreed to pay Valencia $21 million for the 23-year-old Spain defender, who is playing at the Confederations Cup, according to Spanish media reports.
"I don't know anything, nor could I know anything since I'm here with the national team,'' Albiol said after Spain's 2-0 semi-final defeat to the United States on Wednesday. "Now's not the time to talk about it.''
Albiol, who also played at Getafe, would be new president Florentino Perez's first Spanish signing after bringing Cristiano Ronaldo and Kaka to the Santiago Bernabeu.
Albiol was a member of the European Championship-winning team last summer and has made 15 international appearances.
The 1.87-metre centre back played 126 league games in four full seasons at the Mestalla.
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