The 20-year-old was assessed by club officials during the 2-0 defeat to Leeds United in November.
Kelly has made 18 appearances for the Robins during the 2018-19 campaign – more than in the whole of last term – and is highly thought of around Ashton Gate.
England boss Gareth Southgate is also an admirer of Kelly – who has been capped twice at Under-21 level – having invited him to train with the senior team during October's international break.
And ClubCall understand he could be subject of a bid next month as the Merseysiders look to add to their defence.
The majority of Kelly's displays have come at left-back but manager Lee Johnson expects his long-term future to be at the heart of the defence.
That versatility could be among the reasons for Liverpool having an interest, with the club short of options at left-back, while with Dejan Lovren approaching his 30s a new centre-back will soon be required.
The Championship side have a decent tradition of bringing through young defenders, with Joe Bryan's emergence winning him a summer move to Fulham.
Johnson is expecting big things of Kelly going forward and expects him to reach the summit of the game.
He said in October: “I think I have been quite vocal in my admiration of Lloyd Kelly as a footballer.
“I have to say he was absolutely fantastic in the game against Switzerland and so was Jay Dasilva.
“You could really see those two boys had been playing senior football and training with the men.
“Physically in the Championship, Lloydy is 6ft 3in, but he looks a bit slight.
"But if you see him at his own level he looks an absolute beast.
"That athleticism, his height, and even his chest now – we have spent a lot of money making sure he gets the right nutrition and the right supplements and you can really see that coming to fruition now.
“He was a couple of years ago a real beanpole but had that raw potential to be a top athlete.
"Now he is proving that.
“He played centre half for England in a four, with Jay Dasilva at left back.
"It was a really good game and England played really well.
“The concentration levels from Lloyd were good, obviously at centre half he is still learning at Championship level but at left back he has excelled.
“I think he will be a centre half as he ages and progresses and gets that experience but at the moment he is doing a sterling job at left back.”
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