Swansea currently occupy eighth spot - three adrift of the top six - whereas Bristol City lie 10th before the penultimate round of fixtures.
While their chances of breaking into the top six are still highly plausible, Swansea have lost some vital ground over the past couple of weeks and have now been leapfrogged by an in-form Millwall side in the table.
Three wins from seven since the Championship was allowed to resume has severely dented Swansea's playoff dream, and Steve Cooper's men must win here to keep their slim hopes alive before they take on Reading on the final day.
However, Swansea are about to come up against a Bristol City side whom they haven't beaten since the 2010-11 campaign, and the two clubs played out a goalless stalemate in the reverse fixture.
Meanwhile, not many fans could have expected Bristol City's resurgence over the past few weeks, but it may be a case of too little too late for the Robins with two games left to go.
Bristol City were in a rut before Lee Johnson ultimately lost his job in the dugout, but the Robins have taken seven points from a possible nine since Dean Holden took temporary charge of the playoff outsiders.
Despite recording wins over Middlesbrough and Hull City before playing out a 1-1 stalemate with Stoke City on Wednesday, Bristol City are five points adrift of the top six and will need nothing short of a miracle to clinch a playoff spot now.
Indeed, a barren run of nine games without a win before Holden was dismissed seriously damaged the Robins' playoff ambitions, and the Bristol City faithful will most likely be resigned to another case of close but no cigar following their eighth-placed finish last term.
The Robins will be facing Preston North End on the final day of the season - another team that have fallen out of the running for a top-six finish - so Bristol City will no doubt want to end on a high note before they prioritise their search for a new manager.
Swansea City competition form: LDWWLD
Bristol City competition form: LLLWWD
Kyle Naughton was sent off for Swansea late on in the draw with Forest and will not be available for the visit of Bristol City, while Erwin Mulder will continue in goal following Freddie Woodman's hip injury in the defeat to Leeds United.
One positive that Swansea took from the draw with Forest was another goal for the up-and-coming Rhian Brewster, who now has three in his last four Championship outings.
Swansea City possible starting lineup:
Mulder; Cabango, Van der Hoorn, Guehi; Roberts, Byers, Grimes, Bidwell; Celina; Brewster, Ayew
Bristol City possible starting lineup:
Bentley; Benkovic, Kalas, Vyner; Hunt, Massengo, Weimann, Smith, Dasilva; Wells, Diedhiou
We say: Swansea City 2-3 Bristol City
The two clubs will certainly not want to give up hope of a top-six finish just yet, but the odds are stacked against both sides heading into the penultimate round of fixtures. That being said, Swansea are short at the back due to injuries and Bristol City are brimming with confidence right now, so we are backing a slender away win in what promises to be a fascinating affair this weekend.