In contrast, Wednesday are currently nine points adrift of the top six and realistically have little to play with six gameweeks of the season remaining.
Swansea are still in with a shout of a top-six finish, but Steve Cooper's side were forced to settle for a point against Millwall last time out - a result which leaves them four points adrift of the playoff places in eighth.
Cooper would have been extremely disappointed by his side's defeat to basement side Luton Town last weekend, and their failure to record maximum points against Millwall has done them no favours as they endeavour to gain promotion back to the Premier League.
However, with both Preston North End and Blackburn Rovers losing ground in the battle for the top six recently, Swansea will feel that they are well-positioned to try and break into the playoff places with six games remaining, but results must improve immediately.
Indeed, the Swans have only managed one win in their last six in the English second tier – form that is more commonly associated with a side battling relegation rather than vying for promotion.
Swansea cannot rise into a playoff spot with a win on Sunday, but Cooper's side have the chance to leapfrog Derby County into seventh should the Rams suffer defeat against Nottingham Forest the day before.
However, the Swans may enter the weekend's fixtures in ninth if Millwall triumph against Charlton Athletic on Friday evening.
Matheus Pereira bagged a brace for the Baggies after a Charlie Austin penalty broke the deadlock in the first half, and the heavy home defeat leaves Garry Monk's side in mid-table obscurity as the season enters its closing stages.
As things stand, the Owls are nine points adrift of the top six as they lie 13th on 52 points - and the same margin also separates Monk's side from the relegation zone after 40 games.
It is difficult to imagine Wednesday surging towards the playoff places at this late stage of the season, but Monk will be optimistic about his side's fortunes against out-of-form Preston and Queens Park Rangers in the days following their trip to South Wales.
Swansea and Wednesday played out an enthralling 2-2 draw at Hillsborough back in November - with Ben Wilmot equalising for the Swans deep into added time just minutes after Morgan Fox appeared to have won the game for the Owls.
Swansea City Championship form: LDDWLD
Sheffield Wednesday Championship form: WLLDWL
Sheffield Wednesday form (all competitions): LLLDWL
Sam Winnall is carrying a knock and is a doubt, but there are not expected to be many changes to Wednesday's side for the trip to the Liberty Stadium.
Kieran Lee had to settle for a place on the bench against West Brom, but the midfielder is in contention to feature from the first whistle for this one.
Swansea City possible starting lineup:
Woodman; Roberts, Cabango, Wilmot, Bidwell; Byers, Grimes; Ayew, Gallagher, Kalulu; Brewster
Sheffield Wednesday possible starting lineup:
Wildsmith; Palmer, Iorfa, Odubajo; Murphy, Luongo, Lee, Bannan, Harris; Wickham, Rhodes
We say: Swansea City 2-1 Sheffield Wednesday
Wednesday's defensive problems are well-documented - with the Owls having kept just one clean sheet in their last 10 Championship outings. Swansea's recent form has also left a lot to be desired, but we are backing the home side to keep the pressure on the top six with a narrow victory over the Owls.