The Liverpool boss raved about the 20-year-old ahead of this weekend’s English Premier League opener between the 2019/20 champions and newly-promoted Norwich City at Carrow Road.
He said: "They lost good players, or one at least that I know about, but they did sensational business.
"Billy Gilmour is probably one of the biggest Scottish talents for the last 50 years. Bringing him in on loan and then (Milot) Rashica signing from the Bundesliga.
"So they lost (Emiliano) Buendia yes but the replacements they found - and now with the little Greek boy (Christos Tzolis) who came in last week - are good business.
"So it's exciting what they're doing and we have to be absolutely spot on."
Gilmour joined Norwich City from Chelsea this summer in a loan deal that will last the duration of the 2021/22 campaign as the Blues look for their prodigious youngster to get regular playing time.
Having earned rave reviews against the Reds in a break-out performance for Chelsea in March 2020, Gilmour is raring to get started as he hopes to help his new club survive in the harsh world of the English top flight.
"What a way to start a Premier League season," said Gilmour with a smile. "I think just to be back in the Premier League playing against these clubs like Liverpool will be amazing.
"You can really see there is a buzz about the place, everyone is excited for the season to start. We have got a tough opener but we are all looking forward to it. Norwich is a team that should be in the Premier League. We are back and we are hoping to stay."
Gilmour moved from Rangers to Chelsea as a 16-year-old for a “significant fee”, believed to be in the range of £500,000, before signing his first contract as a professional.
He made his full Scotland debut earlier this year in the 0-0 draw against England at Wembley at Euro 2020, where he was named the man of the match.