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Vardy's goal in the 1-1 draw against Manchester United saw him set a new Premier League record of scoring in 11 consecutive matches, eclipsing the mark set by United old boy Ruud van Nistelrooy in 2003.
Should he score at the Liberty Stadium, Vardy will equal an even more historic mark: Jimmy Dunne's English top-flight record from 1931-32 of scoring in 12 successive games for Sheffield United.
And that would be an especially sweet moment for England international Vardy, who grew up a fan of Sheffield United's arch rivals Sheffield Wednesday.
"This is the top-flight all-time record and it's set by a Sheffield United player, so being a Sheffield Wednesday fan I'd love to beat it," Vardy told the Guardian.
While Leicester go into the weekend level on points with leaders Manchester City, Swansea are just four points above the relegation zone following a run of one win in 10 matches.
It has led to speculation about the future of manager Garry Monk, who knows that his side's ability to contain former non-league player Vardy could be a determining factor in the outcome of the match.
"We obviously have experience of coming up through the leagues and we have players that have come through to this level," Monk told his pre-match press conference.
"Our club will appreciate a story like that, but it's our job to maybe put an end to that story."
Manchester City have an opportunity to put pressure on the chasing pack as they visit Stoke City, their fellow League Cup semi-finalists, in the Saturday lunchtime fixture.
With progress assured in both the League Cup and the Champions League, Manuel Pellegrini's side can plough all their resources into the league campaign ahead of a sequence of six matches in 24 days.
"Now it is the most difficult time in the league with games coming thick and fast, one after the other," said City forward Raheem Sterling.
"We basically have to take it slow, win game after game and get a good run going."
- Costa comeback? -
Third-place Manchester United could be forgiven for having their thoughts elsewhere as they gear up for Saturday's home game against West Ham United.
On Tuesday they visit Wolfsburg for a match they are likely to have to win to secure a place in the Champions League last 16, leaving manager Louis van Gaal with a dilemma over who to select for the visit of West Ham.
But injuries have already forced his hand, with Phil Jones, Marcos Rojo, Jesse Lingard and Ander Herrera all doubtful, while Luke Shaw and Antonio Valencia are long-term absentees.
Another manager ruing a long injury list is Arsenal's Arsene Wenger, who will be without star forward Alexis Sanchez and midfielder Santi Cazorla -- to name but two players -- for the home game with Sunderland.
Wenger has become accustomed to losing key performers in recent seasons, but he sought to accentuate the positive side-effects of the situation as his team look to end a run of three matches without victory.
"It's always a disappointment to lose the players at an important moment of the season," the Frenchman told the Arsenal website.
"But on the other hand, it's a great challenge to take for the team and a great opportunity to show that we are ready for a fight and we can deal with it."
Champions Chelsea, languishing in 14th place, will expect to continue their recent improvement at home to a Bournemouth team who have gone eight games without a win and shipped 18 goals in six outings.
Eddie Howe's side could therefore prove ideal opposition for the return of Diego Costa, who is likely to be recalled after spending Chelsea's 0-0 draw at Tottenham Hotspur last weekend stewing on the bench.
While Spurs, who face West Bromwich Albion, remain unbeaten in 13 league games, they are at risk of being outflanked by Liverpool, who trail fifth-place Tottenham by two points and visit second-bottom Newcastle on Sunday.
Saturday (1500 GMT unless otherwise stated):
Arsenal v Sunderland, Chelsea v Bournemouth (1730), Manchester United v West Ham United, Southampton v Aston Villa, Stoke City v Manchester City (1245 GMT), Swansea City v Leicester City, Watford v Norwich City, West Bromwich Albion v Tottenham Hotspur
Sunday (1600 GMT):
Newcastle United v Liverpool
Monday (2000 GMT):
Everton v Crystal Palace