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 is His slave and Messenger.
No doubt that it is unlawful for a Muslim man to have an affectionate relationship with a woman other than his wife because such a relationship leads to committing many forbidden acts, such as looking at her, touching her, being in seclusion with her, meeting her and so forth, and all these are absolutely forbidden.
But if it happens that a man sees a woman accidentally and feels attracted to her, he should fear Allaah and keep his chastity. Such a man is not held accountable for that kind of love. Rather he might be rewarded for his patience and chastity.
As for the natural attraction that the male and female have to each other, then they are naturally born upon this inclination and Allaah created them upon this predesposition, and a person has no control over it.
So, it cannot be said that Islam permitted it, because this is a reality but Islam takes into consideration this natural inclination and so it legislated marriage for great benefits and wisdom and forbade taking lovers as this is a means that leads to corruption, depravity, mischief, intermixing of genealogy and other disadvantages.
Allaah Knows best.