The Swans have reached 40 points for the season and look all but guaranteed of a top-flight place for next term.
The Foxes played first at home to West Ham United on Sunday and appeared to be on course for a sixth straight league win after Jamie Vardy's 22nd goal of the campaign gave them the lead.
Claudio Ranieiri's side had won five of their previous seven league games by a 1-0 scoreline, but the match turned in West Ham's favour when Vardy was sent off for a second yellow card as Jonathan Moss felt that he had dived to win a penalty.
The decision has been largely criticised, but Vardy's fall was theatric and his furious reaction to being dismissed saw him charged with improper conduct by the Football Association. The England international accepted the charge and will now miss the Foxes' next two matches.
Two late goals in two minutes had West Ham in front as Leicester's five-match clean-sheet run came to an end, but Moss then awarded a second penalty of the match in added time that Leonardo Ulloa converted to preserve the Foxes' eight-game unbeaten record.
Spurs responded in resounding fashion by hammering Stoke City 4-0 on Monday night and once again this week it is Leicester to play first on Sunday before Spurs get their chance on Monday at home against West Bromwich Albion.
Sunday's match is Leicester's last before what looks, on paper, like a difficult end to the campaign, with trips to Manchester United and Chelsea either side of a visit from Everton.
Consistent team selection has been one of the many reasons Leicester have done so well this season. Ranieri has made a league-low 25 changes to his starting XI this season in the Premier League, but one of his star regulars, PFA Player of the Year favourite Riyad Mahrez, is without a goal or assist in his last three outings.
Playing Swansea might help, though, as the Algerian's only hat-trick for Leicester came in their 3-0 win over the Welsh side earlier this season, when he became only the third Leicester player to score a Premier League treble (after Ian Marshall and Stan Collymore).
Recent form: WWWWWD
Barring an incredible set of results to end the season, the team from Wales are going to be safe for another year.
The gap to the bottom three is still in double figures, although Sunderland do have a game in hand on the Swans and look in the mood to fight until the very end.
Francesco Guidolin's side could have dented one of the teams below them on Saturday but ended up becoming the first to lose to Newcastle United under Rafael Benitez, going down 3-0 at St James' Park to give the Magpies' hopes of staying up some life.
A win on Tyneside would have been greeted by the club ahead of what appears to be an extremely tough finish to the season. A trip to the leaders on Sunday is followed by matches against other top-eight sides Liverpool, West Ham United and Manchester City.
For Guidolin, he is still unsure of whether he has a long-term future at the Liberty Stadium. The Italian has said that he wants to stay, but names like Brendan Rodgers and Paul Clement have been linked with the role.
Should the Swans finish the season strongly against difficult opposition, it would be hard to dispose of Guidolin, despite the lure of managers like former boss Rodgers.
Swansea have enjoyed just two victories in their last 12 Premier League away games, drawing three and losing seven.
Recent form: WLWDWL
With Vardy out, Ulloa should start alongside Shinji Okazaki in attack, with Ranieri unlikely to make many other changes to his usual formula.
Guidolin, meanwhile, has a fully-fit Swansea squad to choose from and may decide to tinker with his lineup after the disappointing showing on Tyneside.
Leicester possible starting lineup:
Schmeichel; Simpson, Morgan, Huth, Fuchs; Mahrez, Drinkwater, Kante, Albrighton; Okazaki; Ulloa
Swansea possible starting lineup:
Fabianski; Rangel, Fernandez, Williams, Taylor; Cork, Fer; Ayew, Sigurdsson, Montero; Paloschi
Head To Head
Leicester's win over Swansea in December ended a run of eight consecutive home wins in this fixture.
The Swans have won none of their last 11 trips in all competitions to play Leicester (D3 L8), with the Foxes claiming victory in each of the last five.
We say: Leicester 1-0 Swansea
This should be another three points for Leicester, but it is a while since they emphatically dispatched an opponent and another tight 1-0 win could be on the cards.