Five points and five places separate the two sides in the Premier League standings, with the Baggies sitting 13th and Swansea down in the relegation zone.
Curtis has admitted that he is unsure how long he will remain in charge of the team, with the talk linking Marcelo Bielsa to the role cooling down recently and Sheffield Wednesday boss Carlos Carvalhal the newest name thrown into the mix.
Chairman Huw Jenkins would have ideally secured a replacement by Christmas having sacked Monk towards the start of the month, but the issue is not quite as pressing as it might have been due to the team's form on the pitch.
The Swans may have only taken one point from their two games under Curtis to date, but there has been a definite improvement since he took over and an elusive victory may well be drawing nearer.
The performances have been positive, then, but it is the results that need to improve. Since a 2-1 victory over Manchester United that completed an impressive August, Swansea have won just one of their last 14 outings in all competitions, and that came against rock-bottom Aston Villa.
Their current winless streak is seven games, which has seen them plummet down the table and occupy a spot in the relegation zone with just under half of the season gone. Should they fail to win on Boxing Day then it would be the first time that they have gone eight without a victory since the 2013-14 season.
Their recent home form will not fill fans with encouragement that their run is about to end either. They have failed to win any of their last seven home games, scoring in just two of those.
It is goals that have been the major problem for the Swans this term. They have failed to find the back of the net in eight of their 17 matches - more than any other side in the division - while only Aston Villa and Stoke City have scored fewer.
Bafetimbi Gomis has just one goal since August having started the campaign with four in four, and only four others players have found the back of the net for the Swans this term.
Recent form: LDLLLD
West Brom have not found victories easy to come by in recent weeks either, although they can point to a difficult fixture schedule as a big reason behind that.
Indeed, despite only having won one of their last seven, the Baggies will be relatively pleased with how they traversed a difficult stage of the season, taking points off the likes of Arsenal, Tottenham Hotspur and Liverpool.
Things do get easier in the coming weeks, with West Brom's next eight league games all coming against teams currently in the bottom half of the table.
That did not seem to help them last week, however, as a resurgent Bournemouth picked up a 2-1 victory at The Hawthorns in a match that also saw the Baggies finish with only nine men on the field after red cards for James McClean and Salomon Rondon.
It was a disappointing end to a four-match unbeaten streak all against top-half opposition, but with a full complement Tony Pulis will be confident of getting back to winning ways sooner rather than later.
That will be particularly true in away games, with West Brom boasting a better record on the road than they do in front of their own fans so far this season, despite not picking up an away win since October.
No team in the league has conceded fewer on their travels than the Baggies, but on the flip side only Newcastle United have scored fewer than West Brom's six goals in eight games.
They do not have a particularly good record on Boxing Day either - they have won just one of their nine Premier League matches on the day, losing six times.
Recent form: LWDDDL
Pulis will be without McClean and Rondon for the next three matches following their red cards against Bournemouth, which could see Saido Berahino handed a run in the starting XI.
Franck Tabanou will not be available, however, with the French defender not expected to return until next year.
Swansea possible starting lineup:
Fabianski; Rangel, Fernandez, Williams, Taylor; Shelvey, Britton, Sigurdsson, Ki; Ayew, Gomis
West Brom possible starting lineup:
Myhill; Dawson, McAuley, Olsson, Brunt; Gardner, Fletcher, Evans, Morrison, Sessegnon; Berahino
Head To Head
These two sides have alternated between victories over the last six meetings, picking up three apiece. Should the run continue this weekend then Swansea would win.
The Baggies have only won once at the Liberty Stadium in the Premier League, though, with that victory coming in March 2014 when they came from behind to win 2-1.
We say: Swansea 0-0 West Brom
Neither side are big scorers or in great form at the moment, so a stalemate is the most likely outcome. Swansea's three Boxing Day fixtures in the Premier League to date have seen only two goals combined, and it looks set to be another low-scoring affair in South Wales.