The Reds will seal the title if Arsenal lose at home to Crystal Palace on Thursday or if they beat Tottenham at Anfield on April 28.
It looked like being a frustrating day for Liverpool as second-bottom Leicester kept them at bay despite a host of chances for the visitors.
Slot’s men finally made the breakthrough in the 76th minute when Alexander-Arnold lashed home the rebound from close range after Mohamed Salah and Diogo Jota both hit the crossbar.
With speculation mounting that Alexander-Arnold will join Real Madrid when his contract expires at the end of the season, it was notable that the England right-back embarked on a wild celebration of his winner.
Alexander-Arnold earned a booking for ripping off his shirt and planting it on the corner flag after he sprinted to 3,000 jubilant Liverpool fans in one corner of the King Power.
“It took us a long time and, of course, a great moment for Trent after working so hard to come back. To score the goal that makes a lot of difference is very special,” Slot said.
“It’s never hard to dream [of the title] but you see we are really focused on playing Tottenham.”
Liverpool’s title celebration is only a matter of time but Leicester will spend next season in the Championship after their woeful one-year stay in the top tier came to an end with a 23rd defeat in 33 league games.
Fresh from a famous victory over Real Madrid on Wednesday to reach the Champions League semi-finals for the first time since 2009, Arsenal ensured Liverpool would not be able to start their party this weekend.
Mikel Arteta made only three changes from the 2-1 win in the Spanish capital and was rewarded with a dominant display to kill the game off inside half an hour.
“All we can do is delay that moment [Liverpool win the league] from our side to earn the right to finish as high as possible,” Arteta said.
Leandro Trossard was one of those recalled by Arteta and prodded in his eighth goal of the season to open the scoring.
A flowing move saw Bukayo Saka’s cross flicked by Mikel Merino into the path of Gabriel Martinelli to finish to double the Gunners’ lead.
Moments later, Saka was chopped down by an awful challenge from Leif Davis that saw the Ipswich left-back shown a straight red card.
Trossard fired in his second after a well-worked corner before Ethan Nwaneri’s deflected effort rounded off the scoring.
Defeat realistically ends third-bottom Ipswich’s hope of maintaining their Premier League status as they are 15 points adrift of safety with five games remaining and have a significantly poorer goal difference than West Ham.
Chelsea needed two late goals at Fulham to revive their chances of Champions League football next season with a dramatic 2-1 victory.
Alex Iwobi opened the scoring on 20 minutes and Chelsea were meandering towards a damaging defeat until 19-year-old substitute Tyrique George fired in a snap shot from the edge of the box on 83 minutes.
Pedro Neto then completed the comeback with a stunning strike in stoppage time to secure Chelsea’s sixth win in their last 17 league games.
Fifth-placed Chelsea moved above Nottingham Forest, who travel to Tottenham on Tuesday.
Manchester United succumbed to an eighth home league defeat of the season as Wolves won 1-0 at Old Trafford.
Pablo Sarabia curled in a brilliant free-kick 13 minutes from time to hand United a club record 15th league loss this term.
Wolves’ fifth consecutive Premier League win lifts Vitor Pereira’s side up to 15th and level on points with United, who stay 14th on goal difference.
