The highly-rated 20-year-old has featured 16 times for the Bees since making the temporary switch from the Blues in the summer.
He told the Fulham Chronicle: "I love it here. It's great to be getting games and playing good football.
"I had a bit of an injury and a dip in form, but I feel I'm getting better with every game. You want to play in front of big crowds and pick up three points. There's more pressure.
"Things are going well and I'd be willing to stay on. We'll have to sit down before then and see what the best thing is for all parties and go from there."
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