Green debuted for the then-European champions in the UEFA Champions League in November against CSKA Moscow, coming on in the 88th minute in his only senior minutes in club football.
With Bayern preparing their assault for a third straight Bundesliga title, United States international Green is declaring his hand for a prominent place in Pep Guardiola's side.
Green, 19, became the youngest US player to score at a FIFA World Cup finals, on target in extra-time of their last 16 loss to Belgium with his first touch of the tournament in Brazil.
And the teenager wants to convert his international form into the domestic scene, as he yearns for a league berth with the champions.
"I just want to show the coach and the team that I can help them," Green said.
"If I get my chance, I'll try my best. I'm waiting for my chance.
'The relationship [with Guardiola] is very good.
"I feel the trust with him, and it's very important for a young player to feel the trust from the coach. I want to repay the trust from him."
Green said he had no thoughts of requesting a loan away from the Allianz Arena, as he prepares to knuckle down in Munich.
"The most important thing right now is Bayern. I'm not thinking about a loan or something else. I'm playing for Bayern Munich and I want to stay," he said.
The former Germany Under-19 international switched allegiances to represent the US, and he will likely get the chance to play on home soil when Bayern face Chivas Guadalajara in New York on Thursday.
