The 20-year-old enjoyed a productive campaign on loan at Bolton Wanderers last term, making 41 third-tier appearances, scoring five goals and providing five assists.
Bradley impressed Jurgen Klopp during pre-season and earned a place in his first-team plans, however a back injury that the youngster suffered in August means that he is only just returning to action.
The defender featured off the bench for eight minutes in the 4-0 thrashing of LASK Linz in the Europa League on November 30, before playing the entirety of the defeat at Union SG on Thursday in the same competition.
According to TEAMtalk, Burnley are among a number of Premier League and Championship clubs who are interested in signing Bradley during the January window.
It is understood that the Clarets have joined Daniel Farke's Leeds, West Bromwich Albion and Middlesbrough as potential suitors for the Northern Ireland international.
Although the report also names that quartet of clubs, it is claimed that around a dozen sides are keen on the right-back ahead of the window opening.
It is believed that Liverpool and Klopp are willing to send Bradley out on loan for the remainder of the 2023-24 season, as the youngster continues his development.
Ahead of the defender in the full-back pecking order is fans' favourite Trent Alexander-Arnold, who has made the right-back position his own over the past few years.
Consequently - in the short term - it appears that the only way Bradley will earn regular first-team minutes is to move temporarily to another club.
Vincent Kompany's side currently have Connor Roberts and Brazilian Vitinho as options on the right side of their defence, with the latter starting the most recent match against Everton.
Leeds have fielded youngster Archie Gray at right-back for the majority of the campaign, despite the Whites having more natural full-backs such as Djed Spence and Luke Ayling within their ranks.
Bradley was an unused substitute in the Reds' goalless draw at home to arch rivals Manchester United, with Alexander-Arnold starting at right-back as expected.
The youngster will be hoping for some minutes when Klopp's men host West Ham United in the quarter-finals of the EFL Cup on Wednesday - a competition in which the German coach has rotated in so far this season.