Although one may, during this period, convey his desire for marriage through indirect hints or suggestions, it may not be done through an explicit proposal. Says Allah Ta'ala: And there is no blame on you in what you proclaim or hide in your minds concerning betrothal to women.... (2:235) It is likewise forbidden to the Muslim to propose to a woman who is already betrothed to a brother Muslim; the one whose proposal has already been accepted has acquired a right which must be safeguarded in consideration of goodwill and affection among people, especially among his brother Muslims. However, if the first suitor terminates his betrothal or gives the second suitor his permission, there is no harm in proceeding with it. 

Muslim reported that the Messenger of Allah (peace be on him) said, "A Believer is a brother to another Believer. It is therefore not lawful for him to outbid his brother in buying something or to propose to a woman when his brother has done so, unless he gives him permission." And al-Bukhari reported that the Prophet (peace be on him) said, "A man must not propose to anther man's betrothed unless he withdraws or gives him permission."