All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Islam does not approve any type of relationship between a man and a non-Mahram (marriageable) woman outside the framework of marriage which Allaah The Almighty made lawful, as such relationships lead to unfavorable results and evils. When prohibition under Sharee‘ah (Islamic law) is clearly stated, the person’s sincere intention and righteousness are of no effect. When a person is truly religious and follows the straight path, this entails avoiding what is prohibited by the Sharee‘ah. Satan could inevitably lead such a person to commit immorality. Allaah The Exalted Says (what means): {O you who have believed, do not follow the footsteps of Satan. And whoever follows the footsteps of Satan - indeed, he enjoins immorality and wrongdoing.} [Quran 24:21]
Having stated this, it is clear that a girl is not permitted to go out with a non-Mahram man. If he truly wants to marry her, he has to propose to her family and marry her. Otherwise, this relationship with her has to end.
Allaah Knows best.