The Islamic criterion for a good proposal is indicated in the prophetic tradition where Rasulullah Shalallahu ‘alaihi Wa Sallam said:
“If there comes to you (to propose marriage to your daughter) one with whose religious commitment and character you are pleased, then marry (your daughter) to him, for if you do not do that, there will be fitnah (tribulation) on earth and widespread corruption.” (Narrated by Amad)
When the engagement is done, it does not mean that the man and the woman are allowed to be alone without a mahram.
Is a Muslim woman allowed to propose to a man for marriage?
Most of the people in many countries have a mindset that it’s a man who should always make a proposal for marriage and make women feel guilty or ashamed as if they would be doing something wrong and unacceptable by asking for a man’s hand in marriage. For this reason many women wait on the man to propose and sometimes end up waiting for months – sometimes even years go by – and as result the marriage will be delayed.
According to Islam , there is no problem for a Muslim woman to propose to a Muslim man if she knows about a man who has good character, good Deen and who would be a good husband. Islam gives a Muslim woman the right and honor to make such a proposal without feeling guilty or ashamed. 
The best example is from our best role model, Rasulullah, Shalallahu ‘alaihi Wa Sallam, who accepted the proposal from ummul mu’minin Khadijah, Radhiallahu ‘anha, through her friend, Nafisah.
Obviously Allah (SWT) would never have permitted him to accept a proposal from a woman if this act was in any way shameful or improper.
There is absolutely no prohibition in Islam for a woman to propose marriage to a man. It is perfectly fine for you to approach the man in a most honorable way and let him know your intentions by hinting or being flat out about it, or having your guardian (Wali) propose marriage on your behalf to a righteous and suitable man.
It is depending upon the noble custom in your society. It should be done through the proper and reasonable channels and without violating any rules of Shari’ah. So sisters, it is your right to make the first move. If there is a good brother out there that you like as a husband, then don’t be ashamed or afraid to ask for the brother’s hand in marriage.
May Allah bless us. And Allah knows Best.
