The Bavarians are believed to be keen on the Spain international, but Bilbao's asking price as well as interest from Barca and Madrid could prove to be too much of an obstacle
The Bundesliga giants are desperate to strengthen their squad this summer after a relatively disappointing season where they missed out on the league title, Champions League and DFB Pokal, and they see the 23-year-old Martinez as a good addition to their squad.
The Spain international has made over 150 Liga appearances for Bilbao in the past five seasons, and has become one of the most sought-after midfielders in Europe.
Nevertheless, Bayern face a tough task trying to lure the World Cup winner, who can also feature in defence, away from Bilbao.
Martinez has a €40 million release clause, which does not apply if he were to be sold to a non-Spanish team, and Bayern seem reluctant to pay that amount for the midfielder.
The former Osasuna starlet signed a new long-term deal last summer to tie him to San Mames until 2016, and Athletic will reportedly only sell the influential midfielder if the right offer comes along.
Martinez has also attracted the interest of clubs such as Barcelona, Real Madrid, Manchester City and United.