The Belgium international, sent off in south Wales in last season's Capital One Cup semi-final, is expected to be sidelined for two weeks after he was forced off against PSG
Jose Mourinho's men progressed to the semi-finals of the Champions League in midweek, with Demba Ba scoring late on to secure a 2-0 second-leg victory over Paris Saint-Germain that put the Blues through via the away goals rule.
However, a trip to the Liberty Stadium in the Premier League may not fill the Londoners with confidence as they turn their attentions back to the domestic title race.
Chelsea have been held to draws in each of their previous two league fixtures at Swansea and, last season, their hopes of Capital One Cup glory were ended in a dramatic semi-final second-leg encounter in south Wales.
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It would be fair to assume that Charlie Morgan - the ball boy involved in that incident - will not be on duty on Sunday, while Hazard is also likely to be absent after picking up a calf problem against reported suitors PSG in midweek.
Chelsea currently sit two points adrift of Premier League leaders Liverpool, while third-placed Manchester City, who visit Anfield in the undoubted match of the weekend earlier on Sunday, are a further two points back with two games in hand.
Mourinho's charges cruised to a 3-0 win over Stoke City in their last league outing, while Swansea - just six points clear of the relegation zone - slumped to a lacklustre 1-0 defeat at FA Cup semi-finalists Hull City.
Chelsea's last Premier League away trip produced a disappointing 1-0 defeat at Crystal Palace - their third loss in a row on the road in all competitions - but Swansea head coach Garry Monk is keen not to underestimate the challenge that his side face.
"Chelsea are competing for the league, [are] in the semi-finals of Champions League and have one of the strongest squads and best managers in the world," Monk told the press.
"When you look at it like that, we don't have a chance - but you don't think like that, it's something we embrace and it's a chance to showcase what we can do. We have to be confident."
Swansea have no fresh injury concerns but Dwight Tiendalli's illness means that Angel Rangel's starting berth looks unlikely to be in doubt, despite being openly criticised by Monk for his performance last week.
Aside from question marks over the fitness of Hazard, Mourinho should have a full squad at his disposal, although John Terry is thought to be a doubt with a foot injury.