David Moyes wants to sign a centre-back this January but Sky Sports understands that a deal for Mawson is highly unlikely, as Swansea City face their own relegation fight.
Mbemba joined Newcastle from Anderlecht in 2015 and has made 58 appearances for the club, although only seven Premier League starts under Rafael Benitez this season.
The 23-year-old has 38 international caps for DR Congo and would provide Moyes with some youthfulness to go alongside the experience of Winston Reid and Jose Fonte.
Sky Sports adds that West Ham would be happy to include unsettled striker Diafra Sakho as part of a swap deal, which could be an ideal solution for the goal-shy Magpies.
Sakho has yet to make a league start for the Hammers this term and had been in discussions over a £10m move to Crystal Palace which may now collapse, reports Sky Sports.
Neither Mbemba or Sakho are fulfilling their potential at their current clubs, so a part-exchange deal could suit all parties involved, unless Palace still have a say in proceedings.