"Deep feelings" refers to intense emotions or strong emotions that run deeply within someone. It implies a heartfelt or profound emotional experience or attachment. Full definition
The atmosphere is dark and mysterious, with deep feelings of isolation and great music to set the tone. (retronuke.com)
Tell her you are starting to develop deep feelings for her and you want to give the relationship a realistic footing where those feelings can flourish if they are meant to. (datingadvice.com)
Obviously, there are very deep feelings about this on both sides of the discussion. (sbnation.com)