Burn helped the Glovers win promotion to the Championship.
"It's been unbelievable and one of the best seasons of my life," he told the Western Daily Press. "I've made some brilliant mates, played under some excellent management and I've loved playing for Yeovil. I don't want to leave.
"I'll go back to Fulham, do pre-season with them and then see what they're thinking of my progression and what they want to do with me.
"But I'd love to come back here, I'd never turn down a move here. I'll go back and see what happens after a few holidays."