The 22-year-old is into his fourth season in the Elland Road first-team set-up, and can play either as a conventional right-back or in a role further up the flank. He has already amassed 127 appearances for Leeds United and is a player with a bright future.
The Daily Mirror claim Swansea City are readying an £8m January bid for the Essex-born wide-man and also report that Everton are keen on the Leeds United talent.
Arsene Wenger currently has a number of top-quality options to field at right-back, with young Spaniard Hector Bellerin currently keeping out French international Mathieu Debuchy, whilst Liverpool boss Brendan Rodgers has seen Nathaniel Clyne effectively replace departed England right-back Glen Johnson at Anfield.
Leeds United haven’t started the season well under Uwe Rosler, with the Lilywhites collecting just one win from their opening seven Championship fixtures.
The Daily Mirror state that Byram has turned down a new contract, and believe that he could be tempted by a move to Swansea City.