Slaven Bilic's side will be hoping to end their six-game winless run and consolidate their push for a top six finish.
They may not have won since October but the East Londoners have drawn four of those six games and coped admirably with a horrendous run of injuries.
Shorn of the likes of Dimitri Payet, Diafra Sakho, Manuel Lanzini and Winston Reid the Hammers have played out back-to-back 0-0 draws against Manchester United and Stoke City but could easily have come away with six points.
'I think we can get the three points there'
And now fans' favourite goalkeeper Adrian, who was named in the European Team of the Week after his performance against Stoke last time out, has told the club's official website he thinks they will taste three points again at the Liberty Stadium.
“The team defended well (against Stoke and Manchester United), not just me, all the team defended well and I think if we keep a clean sheet we have a chance to win the next game," Adrian told whufc.com.
“If we keep showing the same performance, continue to keep clean sheets and if we are more clinical in attack, I think we can get the three points there (at Swansea).”
The Hammers will fancy their chances of a result given that Swansea are somewhat in disarray after the sacking of Garry Monk last week.
Monk was relieved of his duties after just one win in the last 11 games.
History books favour Swansea
But if the Hammers are to beat the Swans they will have to upset the history books.
That's because the Irons have only won four of the 25 games between the two sides in Wales, drawing six and losing 15.
There's usually goals, though, with this particular fixture averaging more than three goals across the 25 games.
Carroll will be leading the line again for the Hammers and will hope he can get back on the scoresheet after just one goal since his return from injury this season.