All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There is no harm in calling that girl to wear Hijaab and it would be even considered a good act on which you would get reward. The Prophet said: “I swear by Allah! If Allah guides one single man (to Islam) by your efforts, that will be better for you than possessing an abundant number of red camels (a very expensive breed of camels which is considered as the most valuable property in the sight of the Arabs).” [Al-Bukhari and Muslim]
However, this call should not be directly through talking with her over phone or chatting with her. Satan is very eager to push a human being step by step to an evil and unhappy end. Allah Says (what means): {…and do not follow the footsteps of Satan. Indeed, he is to you a clear enemy.} [Quran 2:168]
Moreover, many forbidden relations start by a sight, then a smile, then a word, then a promise, and, at last, the dating. It is also said that huge flames are always from small sparks.
Yet, you may call her towards adhering to Islam by sending pamphlets, cassettes, and useful booklets. You may also recommend some good Muslim sisters to visit her, exhort her, and teach her the rulings of the Sharee’ah.
You may also advise her to listen to Islamic lectures and take part in women Islamic activities that are conducted by Islamic centers. If she follows the right path, then you may marry her, but your marriage to her after her adherence to the Sharee’ah, surely, helps her to be steadfast in her religion.
Allah knows best.