Rene Girard's side have 76 points with two games left and will be crowned champions if they get a better result at home to Lille on Sunday than second-placed Paris Saint-Germain (73) do against Stade Rennes.
Defeat at their Stade de la Mosson would make for a nail-biting finale as defending champions Lille, who are third on 71 points, could narrow the gap to two points.
"It had better be this year because then it is going to be PSG all over the place for seven years, there's no way we'll avoid this," Montpellier president Louis Nicollin, one of the most colourful characters in French football, told reporters.
"I'm so stressed out. We could be eighth, comfortable, having secured our place in the top flight.
"It's stressful because we need to avoid third place and that annoying Champions League play-off. So second would be great. But first...," he added.
Montpellier suffered a bout of nerves two weeks ago when Younes Belhanda hit out at team mate Olivier Giroud for not taking a decisive stoppage-time penalty resulting in Souleymane Camara missing the spot-kick in a 2-2 draw against Evian Thonon Gaillard.
Montpellier, however, bounced back on Monday with a comprehensive 2-0 win at fifth-placed Stade Rennes, with Camara and Remy Cabella, who deputised for the suspended Belhanda, scoring both goals.
"We are warriors, real warriors," said midfielder Benjamin Stambouli.
"[On Sunday] La Mosson will be boiling. They'd better be well prepared."
Lille captain Rio Mavuba believes both Montpellier and PSG could crumble under pressure.
"They have been both fighting for top spot for a long time but they could feel the pressure seeing they may end up in third place afterall," Mavuba told his club's website.
With seven teams within four points, the battle for survival will heat up on Sunday.
Bottom club AJ Auxerre, who are on 34 points and have been in the top flight since 1980, will be relegated if they lose and both AC Ajaccio and Sochaux win, respectively against Olympique Lyon and at Caen.
Four clubs, Rennes, Saint-Etienne, Girondins Bordeaux and Toulouse, will be out to secure fifth place, which would send them into next season's Europa League.
