The Lionesses midfielder signed for the German giants last summer from Manchester City and recently extended her deal until 2026.
Stanway stars for the women's side in the Frauen-Bundesliga, with fellow England international Kane now starring for the men's team.
Both players make regular appearances for their country and help represent the English contingent on the continent.
But despite both players being at Bayern at the same time for almost three months, Stanway says they are yet to meet each other.
Speaking exclusively to talkSPORT ahead of England's UEFA Women's Nations League clash against Belgium, she said: "I love it [at Bayern], I love it.
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"He's done unbelievably since he's joined. I've not managed to watch him live yet but that's in my plans before Christmas.
"I've actually not had much integration with him, I'm sure the media team will want us to do something at some point, but obviously there's been so many games.
"We've been here [St George's Park] for a lot of the time for obviously the last camp, the World Cup as well.
"So yeah hopefully we'll find a time where we can be able to connect because that would probably be the first time I've met him."
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Stanway featured in all but one of their 22 Frauen-Bundesliga matches last season as they went on to win their fifth title.
Over in the men's side, Kane has enjoyed an incredible start to life in Germany having scored 14 goals in his first 13 appearances.
He netted three times in their 8-0 win over Darmstadt on Saturday, the second time this season he has scored a hat-trick.