Wood, 21, came through the youth ranks at Middlesbrough and joined the Swans permanently last year.
Southampton are keen on bringing in the centre-back this summer as Saints manager Russell Martin wants a reunion with Wood whom he signed when he was Swans boss.
However, the Welsh outfit are reluctant to sanction Wood’s exit to their Championship counterparts in the ongoing transfer window.
And Michael Duff’s team have already turned down two offers from the Saints for the England Under-21s star.
Now it is claimed that Wood has still an uncertainly over his future amid the Swans’ intention to keep hold of the defender.
Duff’s side hope that Wood will make a significant contribution to their campaign this season, with the Welsh club eyeing securing a playoff spot.
The star defender has entered the last year of his contract at the Swans and it remains to be seen how his fate will be sealed.
