Claudio Ranieri’s side can turn a dream into reality with one more big performance on Sunday.
And with a seven-point lead over Tottenham and three games to go, they have the luxury of knowing that they may not even need to win to do it, with Spurs having to win all three of their matches to even stand a chance.
For Spurs to deny them, Leicester would need to lose two of their last three, and though they play Chelsea on the final day, they have won seven of their past nine matches and lost just three times all season.
Midfielder Andy King believes Leicester have the ability to cope with the pressure of getting over the line.
“It’s one game at a time – everyone keeps saying it,” he told Leicester’s website. “We’ve got a tough game at Manchester United, who are going for a top four position, which is obviously massive for them.
“We’re confident of putting in a good performance. That will stand us in good stead and we’re looking forward to it.”
Leicester will again be without the suspended Jamie Vardy while United are likely to play their strongest team as they chase a top-four spot.
Five points behind Manchester City in fifth, United could employ the fit-again Wayne Rooney in midfield, as they did in the FA Cup semi-final win over Everton last weekend.
“I think you’re obviously more involved in the game, you have a bigger influence from that position,” Rooney told United’s official website. “I enjoyed it.”
By the time Tottenham go to Chelsea on Monday night, the title race could be over. It could also end at Stamford Bridge if Leicester don’t win and Spurs fail to achieve a better result than the leaders.
Spurs midfielder Son Heung Min says they will fight to the end.
“We have to keep going with our heads up, the season is not finished and we keep going,” he said.
“Leicester will play before us now but seriously we have to look just at us.
“Tomorrow is another day and we have to focus for next Monday against Chelsea. It will be a very difficult game but we will carry on looking forward, work very hard and see what happens.”
At the other end, the battle for survival is a case of one out of three as Sunderland, Norwich and Newcastle all try to stay up.
Just one point separates the trio, though second-bottom Newcastle, who have played a game more, face a must-win match with Crystal Palace.
Sunderland, who moved out of the bottom three last weekend, travel to Stoke while Norwich are away to an Arsenal side still looking to lock down an automatic Champions League spot.
Sunderland manager Sam Allardyce has warned his side not to take anything for granted at Stoke, even if the home side have conceded four goals in each of their past three games.
“I’ve known Mark (Hughes, the Stoke manager) for many, many years … and he will not be a happy man believe you me,” he told Sunderland’s official website.
“We are in good form at the moment and if play anything like we did at Norwich we will give them one hell of a game.
“But I would expect Mark will have Stoke really revved up and he will want to stop this very poor run of performances.”
Third-placed Manchester City are away to Southampton, sixth-placed West Ham travel to West Brom, seventh-placed Liverpool play at Swansea, Everton meet Bournemouth and Watford face relegated Aston Villa in the weekend’s other matches.