Wilfried Bony, Michu and Jonathan de Guzman got the goals as Michael Laudrup's men picked up a shock 3-0 victory at the Mestalla on matchday one in September, but Swansea have suffered something of a blip with back-to-back Group A draws against Kuban Krasnodar.
In contrast, Spanish club Valencia have since gone on a three-match winning streak to be assured of their place in the next round and could be crowned group winners with a victory.
Swansea, though, may not even need maximum points on Thursday to win to seal their progression as a draw between Kuban and St Gallen in the group's other fixture would send them through regardless.
The men from South Wales picked up a 2-1 Premier League victory at Fulham on Saturday for their first win in six in all competitions and currently sit 10th in the English top flight.
Valencia, meanwhile, are 11th in La Liga, with 17 points from 14 fixtures, but are without a victory in their last two fixtures.
Encouragingly for Swansea, Valencia have just two wins from 16 away fixtures against English opposition in European competition, but are unbeaten in five continental fixtures on the road.
With so much at stake for the hosts, Swansea goalkeeper Michel Vorm insists he is not underestimating the magnitude of the occasion in what is the club's first foray into the Europa League.
"That is why you want to be a professional football player – to play these kind of games," Vorm is quoted as saying by Wales Online.
"To qualify for the next round of the Europa League would be amazing, if you think about it.
"Three years ago I came here and didn't know what to expect. Now we are talking about playing Valencia at home to go to the next round.
"I think beating Fulham gives us a positive feeling going into that game and now the aim is to go through to the last 32."
Michu (ankle) is unlikely to be ready for a return to first-team action, while Wayne Routledge (calf) also remains a doubt for Swansea after missing out on Saturday. Former Valencia winger Pablo Hernandez (thigh) could be in line for a start, although Laudrup will not want to rush him back after the Spaniard's short-lived return a few weeks ago.
Valencia have no reported injury concerns. Defender Adil Rami - sent off in the reverse fixture - is currently training with Milan ahead of his January move to San Siro.
