Is it permissible for me to propose to a woman who has been proposed to by a friend of mine, if I seek his permission to do so and he grants it to me?

The problem is resolved by what came in the authentic Hadith from the Prophet, peace and blessings be upon him: "None of you should propose to a woman already engaged to his brother until the first suitor gives up or gives him permission to propose." Based on this, the woman decides to marry whomever she chooses from the suitors.