It stands to reason that having a girlfriend is not the manner of a Muslim. It is forbidden for a male Muslim to have a girlfriend, as it is forbidden for a female Muslim to have a boyfriend.
Tackling this point in details, Dr. Muzammil Siddiqi, former president of the Islamic Society of North America (ISNA) states:
Muslims should have good relations with all people, males as well as females, at school, at work, in you neighborhood etc. You should be kind and courteous to everyone. However, it is not allowed in Islam to take a non-mahram person or persons of the opposite gender as a very close friend. Such friendship often leads to haram. In the Qur’an, Allah mentioned that good men and women are those who marry, do not have fornicating relationships and do not have “paramours” or Akhdan see An-Nisaa’: 25, Al-Ma’idah: 5).
Akhdan are “sweethearts” or for a man a “mistress” and for a woman a “lover”. The Prophet, peace and blessings be upom him, is reported to have stated that “whenever two strangers of the opposite gender are alone with each other, Satan becomes the third one between them.” (At-Tirmidhi)”
So it is not allowed for a Muslim boy to have a girlfriend or for a Muslim girl to have a boyfriend. Howsoever pure the intentions may be, the danger is that it will lead to sin. Or at least they will be alone with each other and spend more time together.
Thus, a Muslim should be friendly with his classmates, boys and girls both; but should not take a girl as his intimate friend. Of course, homosexuality is also forbidden in Islam. So he should not take a boy either as intimate friend in the “gay sense” of the word.
If his friend, not girlfriend, is interested in Islam, by all means help her to become Muslim. He can give her the Islamic books and ask her to attend Islamic meetings and lectures. Let her accept Islam by her own will. Do not force her or put any pressure on her to become Muslim. May Allah bless you and keep you on the right path.
Shedding more light on this, the eminent Muslim scholar, Sheikh Muhammad Al-Hanooti, member of the North American Fiqh Council, states:
A friendship with the opposite sex is not of Islam. It used to be of the Jahiliyyah (pre-Islamic era) style of life. A friendship of the two sexes can never be safe or sex-free. I agree that in some exceptional cases, it could be innocent. But, a law is usually amended for social regulations. There is no law to be customized for a certain person or few people.
The Qur’an and Sunnah guidance for the sexes dealing with each other has a main major issue for which Islam has set principles and rules to govern. It is the desire and lust. The Qur’an prohibits anything that motivates one’s heart in a seductive way towards the other. The Qur’an tells a woman when she speaks to a man to speak in a way that doesn’t show any interest in him lest he should feel seduced to build up an unhealthy relationship. If there is a possibility in any kind of action that it could lead by some percentage into catastrophe, no one will ever take that risk.