If a person has proposed marriage to a woman, it is not permitted for anyone else to offer a proposal to her, because of the hadeeth of Ibn ‘Umar (may Allaah be pleased with him) which states that the Prophet (peace and blessings of Allaah be upon him) said: “No man should offer a proposal of marriage over the proposal of his brother until the first one gives up or gives him permission.”(Reported by al-Bukhaari, 4746).
There follow quotations from Ibn Hijr’s commentary which will shed more light on the matter:
The majority of scholars said: This amounts to a prohibition… The Shaafi’is and Hanbalis said: it is prohibited when the woman proposed to, or her appointed guardian, has stated that she accepts the offer, but if she has stated that she rejects this offer, it is not prohibited. If the second man does not know the situation, then he is permitted to propose marriage, because the basic principle is that proposing marriage is something permitted… If the woman has not answered either way, it is permitted. Al-Tirmidhi reported from al-Shaafi’i that the meaning of the hadeeth is: if a man proposes to a woman and she likes him and accepts, no-one else should propose to her after that, but if he (the second man) does not know that she liked and accepted that proposal, there is nothing wrong with his proposing to her. The evidence for this is the story of Faatimah bint Qays, who did not tell (the Prophet (peace and blessings of Allaah be upon him)) that she had accepted the proposal of one (of two men who had proposed to her). If she had told him, he would not have advised her to marry someone other than the one she had chosen. If there is no word of acceptance or rejection from the woman, some of the Shaafi’is say that it is definitely permitted… Al-Shaafi’i said that in the case of a virgin, her silence indicates her acceptance of a suitor.
The hadeeth was interpretated as meaning that if the first man to propose gives permission to the second, it is no longer prohibited for him to propose. … It was reported from Ibn al-Qaasim, the companion of Maalik, that if the first suitor is immoral, a chaste man is permitted to propose over his proposal. Ibn al-‘Arabi said that this was correct… This is applicable if the woman is chaste, because an immoral man would not be compatible for her, and his proposal would be like no proposal at all.
The phrase “until he marries her”* means until the first suitor has gone ahead and married her, so that anyone else will realize that there is no longer any point in proposing; “or gives up” means that the first suitor decides not to go ahead, in which case it is permitted for the second to offer his proposal.
* Please note these words are in another Rewaaya…