The 29-year-old centre-back has emerged as a target for Newcastle in the final week of the transfer window as the club continue to struggle to bring in defenders this month.
A boyhood Newcastle fan, the defender is believed to be keen on the move, but negotiations with Brighton have not been straightforward.
Brighton rejected Newcastle’s first bid worth £8m but the Magpies are expected to keep trying to sign him in the final days of the window.
Graham Potter is not keen to sell him but at the correct price, Brighton are expected to relent and let the player go.
And it has been claimed that the Seagulls would demand at least £15m before agreeing to sell Burn.
That would mean Newcastle would have to offer close to double the figure they initially tabled if they want to sign Burn.
Newcastle have been left frustrated by what they feel are inflated asking prices set by clubs when they came calling for their players this month.
But Brighton are under no pressure to sell and are expected to hold out for a big fee before agreeing to let Burn go this month.