An opening offer of £8 million for the 29-year-old was swiftly rejected by the Seagulls.
The Saudi-backed Magpies are looking to boost their defensive options in their bid to escape the Premier Division drop zone.
The Toon plan to return with a higher offer after their pursuit of Sevilla’s Brazilian defender Diego Carlos came to an end.
Sky Sports News’ North East England reporter Keith Downie said the Magpies are expected to go back in for Burn and the 6ft 7in centre back was interested in a potential move.
Burn, who was born in Blyth, is a boyhood Newcastle fan and grew up idolising Alan Shearer.
Here’s how Seagulls fans reacted to the news on social media:
@BhaCallum: “Although £15m is probably fair for Dan Burn, I’d be absolutely gutted if he goes, I know when everyone’s fully fit it will be hard for him to keep a starting spot, but he’s been so reliable for us! We Brighton fans really appreciate you Sir Daniel with 9 fingers”
@DorisWanna: “I’ll be more sad if Dan Burn leaves than I was about White. #BHAFC #irreplaceable #BDB”
@Rob_Dennis13: I will 100% miss Dan Burn more than Ben White But if we can get £15m+ we have to take it really #bhafc
@bhafcmodo: “Big Dan Burn is one of our most underrated players. He has been class at cb since we signed him. Wasn't good enough as lwb, but it wasn't his fault, not his position. Hope he stays”
@MikeKing14_: “I mean no offence to Dan Burn whatsoever by this, but who would’ve thought even 6 months ago a rejected bid of a decent amount would have the #BHAFC fan base absolutely buzzing that he’s not leaving that easily. Credit to Dan and the hard work he’s put in during Dunk’s absence”
@MrSamWilson: “When we signed Dan Burn I thought it was a largely pointless move; Championship at best, barely going to get a game. Now, I'd be genuinely sad to see him go. He's excelled under Potter and seeing a 6'7 wingback charging forwards is glorious. £10m is a great deal though”
@humphreys_17: “This Dan Burn news upsets me a lot”
@joeythorpe96: “If Dan Burn leaves go get Joe Rodon”
@tonymgc: “I would be gutted to see Dan Burn leave but wouldn’t begrudge him the chance to earn more money than we could ever give him”
@gregbinstead: “I can’t be the only Brighton fan who A - thinks £10m for Dan burn is an insult the way he’s played this season & B - Doesn’t want him leave”