The 18-year-old made his senior debut for Chelsea FC as the Blues beat Grimsby Town 7-1 in the League Cup third round last week.
The midfielder has been a consistent performer for Chelsea FC’s Academy side in recent weeks and Lampard has clearly been impressed by what he has seen from the teenager in training of late.
Speaking in an interview quoted by Metro, Lampard said: “Billy was brilliant the other day [against Grimsby Town].
“I was delighted with the reaction Billy got during the game and that will make him so good.
“Every training session Billy takes part in he lights it up with energy, quality and angles.
“He’s like an old-fashioned midfield player. I know modern midfield players do it, he’s constantly making angles, berating people even though he’s a young boy, personality in the way he plays, never scared to receive the ball.
“He’s got a really big chance.”
Gilmour officially joined Chelsea FC in July 2017 after initially coming through the ranks at Scottish club Rangers.
His next chance to impress in the League Cup could come when the Blues take on Manchester United in the fourth round of the competition at the end of the month.
Chelsea FC are currently preparing for their trip to Lille in the Champions League on Wednesday night as they look to try and pick up their first European points of the season.
They will then focus on their trip to Southampton in the Premier League before the international break.
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