Former Swansea boss Russell Martin is an admirer of Wood and wants to take him to the south coast this summer.
Southampton have failed with one bid for Wood, but now they have gone back in with a fresh proposal to convince Swansea.
The bid now on the Welsh side’s table is worth up to £10m, including add-ons, and Southampton will hope it is enough to turn Swansea’s head.
It is suggested though that the bid does not meet Swansea’s asking price for the 21-year-old.
Wood, who is an England Under-21 international, only joined Swansea last summer from Middlesbrough.
He had loan stints at Crewe Alexandra and Hibernian while on the books at the Riverside.
Southampton will now wait for Swansea’s response on the bid as they look to get a deal for Wood over the line in the remaining days of the summer transfer window.
