Williamson is among the Championship club’s defensive targets.
The 31-year-old, also linked with Leeds United, is available for transfer this summer.
Williamson joined Newcastle midway during Hughton’s first season in charge at St James’s Park, and he helped the club win promotion back to the Premier League at the first attempt.
But the centre-half’s future lies away from Tyneside after the arrival of Chancel Mbemba from Anderlecht.
There could also be another defensive arrival before the transfer window closes at the end of the month.
Williamson – who has made 169 appearances for United in his five and a half years at St James’s Park – is out of contract next summer.
Hughton, looking to mount a promotion challenge in his second season at Brighton, has identified a number of potential defensive reinforcements.
And Williamson is understood to be on the club’s shortlist.
Meanwhile, Cardiff City manager Russell Slade is looking for United loanee Sammy Ameobi to bulk up.
The 23-year-old is on a season-long loan at the Cardiff City Stadium.
And Slade said: “He can get more strength, for sure, and if he’s going to figure more, which he will do with us, then he’s going to need that going forward.
“We are working really hard with him on all aspects.
“He’s so much to offer, but I think we can get him stronger body-wise, and I think, physically, we can get him fitter.”
Meanwhile, Fabricio Coloccini says he was “proud” to sign a contract extension at Newcastle United.
The club’s long-serving captain agreed an extended deal last week ahead of Sunday’s Premier League season-opener against Southampton.
Coloccini – who had been a target for ex-Newcastle manager Alan Pardew at Crystal Palace – played in the game despite missing all United’s pre-season games with an Achilles problem.
“I had a few offers to leave the club, but I said my first choice is to be here,” said Coloccini. “I felt proud because – I want to be here. I feel part of this club and this city. I expect to be fit and play every game.”
On his longer-term future, Coloccini added: “I’d like to finish my career in Europe, maybe here.
“I try to speak in the present. I have a contract for two years, but in the future I don’t know what will happen.”