The Saints are desperate to retain their star right-back, but with Arsenal interested they may be unable to do so.
If they do lose the 20-year-old, Byram is seen as a top class alterative.
The Leeds youngster, also 20, has emerged as one of the Championship’s top talents this term after establishing himself as a first-team regular at Elland Road.
The former Premier League giants are also loathe to lose their starlet, but if their proposed takeover hits the rocks then financial worries may force their hand.
Maurico Pochettino has also been further boosted by claims that Byram has the correct temperament to slot into the Hampshire outfit’s squad.
If Chambers does leave then Nathaniel Clyne is the natural choice for the position, but the current Whites man is seen as a player who can challenge him for the berth.
Arsenal are looking at the Southampton youngster, while reports also indicate that Manchester United are keen.