A Radamel Falcao double, Bernardo Silva's goal and an own goal by Junior Alonso put the principality side on 89 points with two games left while Paris St Germain, who prevailed 5-0 at St Etienne, are on 86 having played one more game and with a much less favourable goal difference.
Monaco will officially clinch their first title since 2000 if they avoid defeat at home against St Etienne on Wednesday in a game that was postponed last month.
Bottom club Nancy will be relegated or at least will need to go through the playoffs to salvage their place in Ligue 1 after they lost 2-0 at Dijon.
Monaco were quickly on the right track as Falcao put them ahead on six minutes when the Colombian striker headed home from a Thomas Lemar cross.
The home side doubled the tally on the stroke of halftime, Silva tapping in from close range after being set up by Kylian Mbappe, who had slalomed into the visitors' defence.
Monaco, whose starting 11 is the youngest of the potential champions in the five big European leagues, wrapped it up in the 69th minute when Falcao fired home from another Mbappe assist.
Alonso scored an own goal one minute from time, leaving Monaco on the verge of being crowned champions after a remarkable season in which they also reached the Champions League semi-finals.
PSG needed to match Monaco's result to maintain a very slim hope of retaining their title and they enjoyed a goal rush at Geoffroy Guichard, whose crowd paid tribute to coach Christophe Galtier, leaving after eight years in charge.
PSG's goal difference of +56 compared to Monaco's +73, however, means that there is virtually no chance for Unai Emery's side to leapfrog the principality side.
Edinson Cavani scored a double to take his league tally to 35 goals this season while Lucas also bagged a brace and Julina Draxler completed the win in the last minute in a one-sided encounter.
Nice are third on 77 points despite a 2-0 home loss to Angers and Olympique Lyonnais secured fourth place and a spot in next season's Europa League with a 3-1 win at Montpellier.
(Reporting by Julien Pretot, editing by Pritha Sarkar)
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