The 85,00-seat stadium was inaugurated in 1947 and was named after former Blancos president Santiago Bernabeu Yeste.
However, Maria Gahan, head of Microsoft Spain, has now revealed that Madrid is keen to sell the naming rights for its home ground to the highest bidder.
"They have offered us, and other companies, the possibility of renaming the stadium,” she told Antena 3.
“We’re in talks, and that sums up where we are."
Current Madrid president Florentino Perez has already spoken of his intentions to find a sponsor for the iconic arena, admitting last month that a number of potential partners had already been approached.