It’s in the books.
Brienne of Tarth is in full on, undeniable, sexually attracted, romantic love with Jaime Lannister.IT GOES LIKE THIS...
If Brienne loved Renly Baratheon:
Brienne dropped to her knees. “If I must part from Your Grace, grant me the honor of arming you for battle.”
Catelyn heard someone snigger behind her. She loves him, poor thing, she thought sadly. She’d play his squire just to touch him, and never care how great a fool they think her…(Catelyn III, ACOK)
Renly Baratheon had been more than a king to her. She had loved him since first he came to Tarth on his leisurely lord’s progress, to mark his coming of age. (Brienne I, AFFC)
Did you sing for Renly? She had not, not ever, though she had wanted … she had wanted …(Brienne IV, AFFC)
the bitter tears she shed the night her king wed Margaery Tyrell (Brienne VI, AFFC)
…And then Jaime replaces Renly in her mind:
And when the shadow sword sliced through the green steel gorget and the blood began to flow, she saw that the dying king was not Renly after all but Jaime Lannister, and she had failed him. (Brienne II, AFFC)
Would that Jaime had come with me, she thought … but he was a knight of the Kingsguard, his rightful place was with his king. Besides, it was Renly that she wanted. (Brienne IV, AFFC)
…And another of her former suitors (Red Ronnet Connington) becomes Jaime:
As he walked away, the griffins on his cloak rippled and blurred and changed to lions. Jaime! she wanted to cry. Jaime, come back for me! (Brienne VIII, AFFC)
We can conclude Jaime has replaced Renly in Brienne’s affections. This is not simply an example of Brienne’s loyalty changing. Brienne’s last oath was to Catelyn Stark, but it is only Renly’s face we see changing to Jaime’s—never Catelyn’s—indicating that these are all references to Brienne’s romantic life alone.
But one could argue Brienne’s love for Renly fell into safe, juvenile crush territory.SO HOW DOES BRIENNE'S RELATIONSHIP WITH JAIME
DIFFER FROM HER RELATIONSHIP WITH RENLY?