It’s stated in the Kuwaiti Encyclopedia of Islamic Jurisprudence that:
“The majority of scholars are of the view that it not permissible to seek a woman in marriage if she is already engaged to another man. This is based on the Hadith of `Abdullah ibn `Umar who quotes the Prophet, peace and blessings be upon him, as saying: “No Muslim is allowed to seek a woman for marriage while she is already engaged to his fellow Muslim, unless the betrothal has been cancelled or the betrothed gives the new suitor the permission.” The reason for this injunction is to prevent hatred, feud and friction that might ensue from proposing to a betrothed. The Shafi`isHanbalis are of the view that this is Haram especially when the subsequent suitor knows about the first and binding proposal.
But it’s to be stressed here that the first proposal must be pending, i.e. it must be in the process. That is why the Shafi`is stipulated that the first person should have been given an open promise of marriage in a valid engagement and that the second person is aware of the impermissibility of making an offer of marriage to a woman already engaged.
However, the Hanbalis adopt the view that even if the promise given to the first person is indirect, it becomes impermissible for the second person to propose to the same woman.
The Malikis adopt the view that it is impermissible to make an offer of marriage to a woman already declared by herself or her guardian as being engaged to a certain man who is not deviant, even if the dower is not specified yet. Some Malikis stipulated that the dower should be stipulated, otherwise, the second offer is not impermissible.
In conclusion, it is to be said that it is impermissible for a person to make an offer of marriage to a woman who is already engaged to another.”
Almighty Allah knows best.