Is it forbidden for the heart to become attached and drawn to someone without exchanging any words other than the greeting of Islam?

Love is a matter of the heart that a person does not control. Its ruling is tied to its cause and effect. If a girl develops an attachment to a non-mahram (definition) man without seeking it, and it does not lead to any forbidden actions such as looking, corresponding, or dating, then there is no sin upon her for this love. Ibn Taymiyyah mentioned that whoever is afflicted with passionate love (ishq), but remains chaste and patient, will be rewarded for their piety. Exchanging greetings of peace (salam) between a girl and a non-mahram man is forbidden if there is a concern of temptation (fitna). However, exchanging it is permissible provided there is no fitna.