The American computer company were first reported to be in preliminary talks with Los Blancos last month to sponsor the planned renovation of their stadium.
And the head of Microsoft’s Spanish division confirm that rumoured talks were underway.
“We are talking,” Maria Garana told Antena 3.
“We have an excellent relationship with Real Madrid and in fact recently we signed an agreement with its [charity, Real Madrid] foundation.
“They have proposed to us, and to other companies, renaming the stadium, but we are only talking about this possibility.”
Emirates Airlines are also rumoured to be in negotiations with Real Madrid over naming rights for the Bernabeu.