“I am incredibly grateful to Bayern. Thankfully, my time here isn’t over yet,” Stanway said in a club statement on Saturday.
“The decision to leave was incredibly difficult. I definitely didn’t make it lightly. I’ve made friends and memories here that will last a lifetime, and I’ve been able to develop enormously as both a player and a person.
“I will give absolutely everything for Bayern and our sporting success until the very last day – just as I have for the past three and a half years.”
Should Arsenal agree a deal with Stanway, it would be regarded as one of the biggest transfers of the January window.
Arsenal are looking to build a squad capable of winning the Women’s Super League, having lifted the Champions League trophy in May, and are working to secure additions for the summer.
Manager Renee Slegers also signed a new three-year deal this week.
