The former Chile boss has supposedly told the Basque side that he will say farewell to the club if they cash in on the versatile midfielder, who has been linked with moves away
The Spain international is continually being linked with a move to a bigger club, and both Barcelona and Bayern Munich are closely monitoring the midfielder's situation.
Martinez's agent revealed earlier this week that his client is open to a move to the Bundesliga giants, but if it were up to the trainer, the 23-year-old would be going nowhere.
Bielsa has reportedly even told the Bilbao president that he will step down if they decide to cash in on Martinez this summer, and a transfer seems increasingly unlikely following the latest developments.
The 57-year-old joined Bilbao in the summer of 2011, and guided them to Copa del Rey and Europa League finals in his first season at the helm.
He was believed to be on his way out of the Basque side earlier this summer after a dispute with the club's board of directors, but eventually opted to stay put.