The Argentine striker has struggled to make an impact at the DW Stadium since his £6million arrival in the summer of 2010.
The 27-year-old is still waiting for his first Premier League goal but is set to feature against the Cherries in an FA Cup third-round replay on Tuesday evening.
And Martinez wants to see a willingness from Boselli to do all he can to press his claims for a first-team spot.
"Each time you are on the pitch you need to be ready to take your opportunity and be at your best because each time you are on the pitch you are playing for your career," said Martinez.
"You need to grab the opportunity with both hands - not just Mauro but every player."