That's according to the Daily Mail, who claim that a £10 million bid could be on the horizon.
The Clarets failed with an effort to sign Fry a couple of years ago, but are understood to be interested in rekindling their interest in the centre-back, with James Tarkowski and Ben Gibson both expected to leave Turf Moor in the coming months.
Tarkowski is out if contract with the club next summer, but is yet to agree to a new deal, and could be sold at the end of the season to prevent Burnley from losing him on a free transfer in 2022.
Likewise, Gibson could be offloaded on a permanent basis after enjoying a successful loan spell with Championship leaders Norwich City.
With that in mind, there could be room for another defender to join the ranks at Turf Moor, and Fry is understood to be a prime candidate.
Middlesbrough boss Neil Warnock is said to be reluctant to part with the 23-year-old, however, and for good reason.
According to Whoscored, Fry has been the second-highest player in Boro’s squad this season, with an average match rating of 7.06. That figure is higher than any Burnley player has averaged this term.
Nobody in Warnock’s side has recorded more clearances than Fry either, with the defender averaging 3.9 per game – a useful trait for any potential Burnley player considering that both Tarkowski and Ben Mee have averaged more than 4.3 per match in 2020/21.
We’ve gathered the rest of today's Premier League speculation below...