Jurgen Klopp revealed in his pre-Southampton press conference that there is a “possibility” the 20-year-old could go out on loan next season and Turf Moor has since emerged as a potential destination.
The Liverpool boss also insisted that “no player has impressed” him more than Carvalho this season, praising his “work ethic” and attitude in training.
Vincent Kompany’s side could look to capitalise on Carvalho’s situation, who has played just eight minutes of Premier League football since the turn of the year.
Football Insider have reported that the Clarets are “keen” on signing the youngster this summer and are “open to both permanent and loan options” in the transfer window.
Burnley are said to be searching for a versatile attacking midfielder, a profile which the Portuguese under-21 international would suit and a position not typically associated with Klopp sides.
Carvalho joined the Reds from the previous Championship winners Fulham for £7.7 million last summer and he got his Liverpool career off to a positive start by registering 16 appearances in all competitions prior to the World Cup.
His involvement has since dwindled, however, leading to suggestions that a loan move could benefit all parties in 2023/24.
Klopp lauded Carvalho as he addressed the media ahead of the season finale at Saint Mary’s, but did hint that he could be sent to get minutes and experience elsewhere next season.
“I think there is a possibility that maybe Fabio will go on loan or whatever. We will see,” he told reporters.
“The thing is, this was not Fabio’s best year of his career, clearly, in a very young career, but it might have been his most important.
“No player has impressed me more than Fabio, that’s the truth.”
His short-term future remains to be seen, but the manager clearly values Carvalho’s determination in training despite spending the majority of the campaign on the periphery.
Carvalho will be keen to spend more time on the pitch after the summer break, be that at Anfield or further afield.