Spain international Martinez - who can play in defence and midfield - could enjoy a dream debut season with Bayern chasing a treble at home and abroad.
They are 20 points clear of Borussia Dortmund at the top of the German standings and hold a 3-1 lead over Arsenal before the second leg of their Champions League last-16 tie at Munich's Allianz Arena on Wednesday.
They also face Wolfsburg in the last four of the German Cup next month.
"We are doing well in the league, the Champions League and the German Cup," said Martinez, who is set to be joined at Bayern by fellow Spaniard Pep Guardiola when the former Barca coach succeeds Jupp Heynckes this summer.
"I feel very good, more and more incorporated into the team. And the team also feels more comfortable with each passing game. We hope we can continue like this.
"I have adapted well because people have been very welcoming. I was scared to come to a new city, with a new language, but I feel really good here. My team-mates have helped me integrate so well, it's as if I have already been with them a long time."
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