Is it permissible for a Muslim woman to ask a man to marry her?

It does not contradict modesty for a woman to offer herself to a righteous man, trusted in his religion and character. Indeed, a woman did this to the Prophet, peace and blessings be upon him, and Al-Bukhari titled a chapter "The woman offering herself to the righteous man." And one of the two daughters of Shu'ayb said to her father concerning Musa, peace be upon him: "One of them said, 'O my father, hire him. Indeed, the best of those you can hire is the strong and trustworthy.'" It is preferable for the woman to hint to her guardian about her desire. However, caution must be exercised against being lenient in addressing men or sitting with them.