The Bavarian giants have been engaged in discussions with the La Liga outfit regarding the 23-year-old, who has also been attracting interest from Barcelona and Manchester City.
Chairman Uli Hoeness admitted that Martinez's fee is "madness", but feels that the club have "raised the bar" with the transfer.
"FC Bayern have raised the bar and have the means," said Hoeness. "You have to admit this amount is madness [but] the board of directors has given the green light."
Martinez, who has eight caps for Spain, joined Bilbao from Osasuna in 2006.