Praise be to Allah.
Allaah makes it easy for the one for whom He wills happiness to find it. Perhaps Allaah wills that for you by means of this person who is calling you to Islam and by means of your getting in touch with us so that you may be guided to what is best for you in this life and in the Hereafter.
Islam does not allow any illicit relationship between a man and a woman. Allaah has established marriage as the legitimate means for satisfying sexual desire, and through marriage a man and woman form a family based on the laws of Allaah, and their children are legitimate.
We will not tell you that hijab (the veil) is not obligatory, and we will not tell you that Islam excuses you from wearing it. Rather we will tell you that you should not let the idea of wearing hijab form an obstacle to your entering Islam. You have to start by saving yourself from your current situation and enter into that which Allaah loves and is pleased with, which is to believe in Him alone (Tawheed) and to bear witness that Muhammad (peace and blessings of Allaah be upon him) is His Messenger. After you enter Islam and faith becomes established in your heart, you will have the opportunity to study and find out for yourself everything that Allaah likes, so that you can do it, and everything that He hates so you can give it up and avoid it.
We advise you sincerely from the bottom of our hearts to choose that which is best for you, not so that you can marry a Muslim man, but for your own sake, and for your own happiness and salvation from the punishment and wrath of Allaah. What you are going to choose is nothing other than the religion of the Prophets of old. It is the religion of Adam, Noah, Abraham, Moses and Jesus. All the Prophets bore witness that God is One, and they denied that He has any partner, wife or son.
Allaah accepted the Covenant from all the Prophets that they would believe in our Prophet Muhammad (peace and blessings of Allaah be upon him) and that they would support him if he was sent during their lifetimes, and He commanded them to tell their nations to do likewise. Allaah made the message of Muhammad (peace and blessings of Allaah be upon him) a message to all mankind until the Hour begins [i.e., until the Day of Judgement comes], whereas the Prophets before him were each sent only to their own people.
So do not hesitate. Hasten before your time is up and death comes. Choose the path that leads to happiness in this world and in the Hereafter. May Allaah make you a Muslim woman and a righteous wife who will establish a home and family based on Tawheed (belief in the Oneness of Allaah) and obedience. We ask Allaah to guide you and support you.
Please also see the answer to question no. 3023.