It looks certain the new bid will test the mettle of the new Saints interim chief operating officer Gareth Rogers.
Southampton chairman Katharina Liebherr’s determination not to sell any stars this month could be a potential obstacle for any of Shaw's suitors, with Chelsea also linked with a move for the full-back.
Liebherr said this month: "The club has no plans to sell any of the squad during the January transfer window.
"The manager and the team have my full support.”
Southampton have put a huge £30m price tag on their prized asset, as revealed by StarSport this month.
That fee would be the highest sum ever paid for a full-back, beating the £29.5m Barcelona splashed out to sign Dani Alves in 2008.
Full story: Daily Star