The 19-year-old, a product of the Academy set-up at Elland Road, joined earlier this month on an initial one-month deal and has started all three games so far.
Rovers manager Les Parry said: "Liam has done really well since he joined us on loan and I'm pleased to have extended his stay until January.He's a bright, young footballer with plenty of ability and potential who has fitted in brilliantly since he arrived.
"I'd like to thanks Leeds United manager Simon Grayson for allowing him to stay with us."
Source: PA
Source: PA