The Welsh club's current record for reaching the fabled milestone is March 2 during the 2012-13 season, but a win at Burnley would see them celebrate St David's Day safe in the knowledge they are all but assured of a place in the top flight next term.
"It's a big motivation for us," said manager Garry Monk. "We have to now use that and go on and do well. We know it will be an extremely tough game and that it won't be easy.
"Burnley are a very fit and intense team to play against. We have to be ready for the battle and match them in every way while also showing our quality."
Swansea completed their first league double over Manchester United with a 2-1 victory at the Liberty Stadium last weekend, having beaten Louis van Gaal's men by the same score at Old Trafford on the opening day of the season.
"Of course last weekend was a fantastic result and performance," he added. "The players have obviously been full of confidence this week but we know that confidence can be taken away very quickly at this level.
"It was a fantastic result and a good display. As I said before the game, it was important that we got a good performance at the weekend to take into the last 12 games of the season."
Burnley picked up an impressive result of their own last time out with a 1-1 draw at league leaders Chelsea, although the performance was overshadowed by the controversy that surrounded a red card for Nemanja Matic.
The Serbian midfielder reacted angrily after being caught by the studs of Ashley Barnes, with Chelsea believing the Burnley man should have been sent off instead.
Manager Jose Mourinho and the club subsequently highlighted four instances in which they felt referee Martin Atkinson made the wrong decision.
"The biggest shame last week is that I thought we delivered a very good performance at one of the hardest places to go in the country," Burnley boss Sean Dyche told the Burnley Express. "It's just what it is, but we know the performance level, and we were very pleased with it.
"Once again we're showing signs of improved performances. It's about turning that into winning football now. If we keep putting in performances like that, it bodes well.
"There are no guarantees, and every game is a challenge. Swansea are a good side who are going well. They seem to have a nice feel about them, and Garry Monk has done a good job since taking over."
Swansea are still without Kyle Bartley (knee), while Nathan Dyer will be hopeful of facing the club where he spent a brief loan spell in 2005 after being left out of the squad completely for the United clash.
Burnley, meanwhile, are missing long-term absentees Kevin Long (knee), Dean Marney (knee) and Matthew Taylor (Achilles).
