Your heart goes out to somebody
Definition 1 of 1
Pro Tip 1/3Emotional Support
Used to express empathy, especially during tough times or tragedies. 
When I heard about the earthquake victims, my heart went out to them.
Pro Tip 2/3Not Literal
This phrase is figurative; your heart doesn't literally move towards someone. 
Despite the distance between us, my heart goes out to you in your time of loss.
Pro Tip 3/3Non-Romantic
It doesn't imply romantic feelings but general compassion for someone's situation. 
When she failed the exam, my heart went out to her.