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The Wales international is open to making the switch ahead of the European Championship qualifying play-offs.
Roberts, 28, has made 88 appearances for the Clarets since joining from Swansea in 2021.
Leeds United are in discussions with Burnley on deadline day for right back Connor Roberts
The Wales star is open to making the move ahead of the Euro 2024 qualifying play-offs
Roberts was introduced for the final 31 minutes of Wednesday's 3-1 defeat to Man City, which left the Clarets seven points adrift of safety with just 12 points from 22 matches.
If he was to make the move, he would join an in-form Leeds side who are just two points off second-place Ipswich as they look to secure an immediate return to the Premier League.
Roberts would hope to secure regular gametime at Elland Road ahead of Wales' crunch Euro 2024 qualifying play-off against Finland in March, with the winner of that tie set to play the winner of Estonia vs Poland for a place at this summer's tournament in Germany.
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