Is it permissible for a woman to offer herself in marriage to a married man, and ask him to marry her, following the example of some of the wives of the Messenger of Allah, may Allah's prayers and peace be upon him, even if she does not know of his desire to marry again?

It is permissible for a woman to offer herself in marriage to a righteous man, even if he is already married, provided that there are no Shar'i prohibitions such as impermissible mixing. This should be done with caution not to corrupt the husband against his wife, nor to stipulate the divorce of his first wife. The desire for marriage can be conveyed through her mahrams or a letter, while observing modesty and chastity.