Having roped in Maxwel Cornet from Lyon, Clarets boss Sean Dyche is keen on adding one more full-back to his backline before transfer window slams shut today.
Dyche zeroed in on Swansea right-back Roberts and Burnley have been locked in talks with the Championship side over a move for him.
And with the clock winding down on the window, Burnley have made positive strides towards landing their target and have agreed on a fee with the Swans for Roberts.
Roberts is poised to move to Turf Moor in the coming hours and complete a deadline day move to the Premier League.
The Wales international has entered the final year of his deal at the Liberty Stadium and Swansea are now set to bag a fee from his departure instead of potentially seeing him leave for free next summer.
Roberts rose through the ranks at Swansea, breaking through to the first team and now could find himself playing top flight football for Burnley post the international break.
The 25-year-old was recuperating from a groin injury and is yet to feature for Swansea this season but returned to training last week.