The Whites opened their season with an entertaining 3-2 win away at Bolton Wanderers, and manager Thomas Christiansen may still be keen on more defensive additions after a shaky afternoon at the back.
Leeds have already added Vurnon Anita and Matthew Pennington to their defensive options, whilst Manchester United's Cameron Borthwick-Jackson is poised to sign on a season-long loan deal too.
However, Leeds have been linked with a move for Bristol City's Joe Bryan for some time now, and The Mirror claim that they are now willing to offer up £2million to sign him this summer - but so are Championship rivals Bristol City and Fulham.
Bryan, 23, was born in Bristol and came up through the ranks at Ashton Gate, with the defender racking up close to 200 appearances for the Robins in all competitions whilst starring either as a left back or left wing back.
Having impressed so much in the Championship though, Bryan has attracted major interest, and Bristol City may have to fend off interest from three of their rivals before this month's transfer deadline.
Two questions spring to mind though. The first is that Leeds are signing Borthwick-Jackson to fill the gap left by Charlie Taylor's exit to Burnley, and with Gaetano Berardi also featuring at left back, it's hard to see the Whites investing in another left back right now, unless Berardi moves over to right back and Luke Ayling to centre back.
The second is that Bristol City are under little pressure to sell one of their prized assets, and letting him go to a Championship rival for just £2million would be a huge surprise, especially given owner Steve Lansdown's wealth and subsequent investment into the club.
Would you like to see Leeds sign Bryan?