Southampton target Leeds United young gun Byram

Southampton manager Ronald Koeman confirmed on Saturday that an offer for Byram – believed to be in excess of £4m – had been turned down by Leeds amid a mounting battle to keep him at Elland Road beyond the end of the month.

United set Byram’s valuation at around £8m a year ago and are unlikely to accept considerably less in this window, despite his injury problems last season, but Sunderland and a number of other Premier League clubs are also interested in the teenager and further bids are likely before the summer market closes on September 1.

Byram is not thought to have submitted a formal transfer request but the YEP understands that his agent has told Leeds that the defender would want to consider suitable offers to move to the Premier League.

Southampton have money available to them after raising huge fees through the sale of several first-team players this summer but they are yet to up their offer for Byram, whose contract at Leeds runs to June 2016.

The south-coast club see Byram as a potential replacement for Calum Chambers, the young defender sold to Arsenal in a £16m deal last month.

Speaking after Southampton’s friendly against Bayer Leverkusen on Saturday, Koeman said: “We lost Calum Chambers to Arsenal. (Byram) was a player we had on the list and it’s true that we had a bid for him, yes.

“What I heard was that Leeds didn’t accept it.”

Leeds signed another right-back, Gaetano Berardi, from Sampdoria midway through their pre-season campaign but Byram was used in United’s first game of the new Championship term at Millwall on Saturday, completing 90 minutes in a 2-0 defeat.

Leeds owner Massimo Cellino, who has already sold former club captain Ross McCormack in an £11m transfer to Fulham, is under more pressure to improve the squad available to head coach David Hockaday after the collapse of a bid for Juventus centre-back Frederik Sorensen.

United pulled out of talks with Sorensen late on Friday evening after losing patience with the player’s representative. The club are understood to have believed that an agreement was in place and ready to sign on two occasions but were subsequently met with further financial demands. Sorensen’s agent was unavailable for comment.

Leeds have looked seriously at two other centre-backs in the past month – Chesterfield’s Liam Cooper and Catania’s Giuseppe Bellusci – and they are back in the market for new defenders after failing to tie up Sorensen’s move. Head coach David Hockaday admitted that additional signings were necessary after watching Leeds start the season with a loss to Millwall, saying: “I’m head coach of a group of players which we know we need to strengthen. We have to show patience with getting new players in and at the moment we are. I can’t magic players up and I’ve got what I’ve got. I’ll work with that.”

Hockaday’s line-up at Millwall was weakened by the loss of midfielder Tommaso Bianchi to suspension and striker Steve Morison to a calf strain.

Morison’s injury denied him an appearance against his former club and Hockaday said: “We had a practice game on Thursday and he took a kick on his calf.

“We were hopeful he’d start but we couldn’t risk him because we’re down to the bare bones a bit.”