Strengthening in the centre-back area is one of the prime objectives of manager Eddie Howe and the Magpies have seen negotiations crumble for Sven Botman and Diego Carlos.
The Magpies have now turned their attention closer to home in the form of Burn, who is said to be open to moving to St. James Park.
They suffered a setback though as the Seagulls refused their initial offer for the centre-back of £8m but Newcastle are determined.
The Magpies have gone back and tabled an improved bid for the centre-back in the hopes of bringing him to St. James Park before the window closes.
The terms of the new offer specify that the Magpies have offered the Seagulls £10m in addition to bonuses.
Newcastle are in for a busy backend of the window as Howe is aiming to get in the door not only Bruno Guimaraes but also two centre-backs and possibly a left-back and a striker.
It remains to be seen what the Seagulls’ response is to the new offer for the centre-back, who has 13 appearances in the Premier League this season.