That scenario would see them join already-relegated opponents Angers in the second tier next season.
Match preview
Following the relegations of Angers, Troyes and Ajaccio, just one spot is left to be decided on the final day of the Ligue 1 season.
It is a straight shootout between Nantes and Auxerre, and despite being two points adrift, the Canaries are the favourites to stay up.
That is thanks to them facing the whipping boys of Ligue 1 this season, while Auxerre have a tricky test against second-placed Lens.
A Nantes win combined with Auxerre failing to win will see them stay up thanks to their superior goal difference.
However, winning is something Nantes have not done much of this season, having not tasted victory in any of their last 14 matches.
With four teams being relegated this season instead of three, it is apt that the worst-performing 17th-placed side in French top-flight history could be the ones to go down, as the league transforms into an 18-team division next season.
Nantes' six wins this season is the lowest tally of any side placed outside the bottom three in the league's history, and it is a record low for the club.
Their 2-0 defeat at home to Strasbourg at the start of the month saw the Nantes hierarchy hit the panic button and sack Antoine Kombouare with just four games remaining.
His replacement Pierre Aristouy has not managed much of a turnaround either, taking just one point from his three games in charge so far.
It has been a rapid fall from grace for Nantes who were in Europe this season after winning the Coupe de France last season.
They could become the third side in the 21st century to be relegated despite starting the season as a domestic cup holder, after Strasbourg in 2006 and Guingamp, who were relegated from Ligue 2, in 2010.
Despite Angers' difficulties this season, Nantes have not enjoyed much success against them in recent years, winning just two of the last nine encounters.
They are also winless in the last four home games against their upcoming opponents despite usually having a great record, after initially winning 18 of their first 19 league meetings with Angers here.
It has been a rotten season for Angers, but is ending with something of a flourish, so much so that caretaker manager Alexandre Dujeux has signed a two-deal to stay on with the club in Ligue 2.
Despite taking just eight points from his 12 games in charge, Angers did perform bravely in narrow defeats to Paris Saint-Germain, Monaco and Marseille.
They could still match the all-time Ligue 1 record for matches lost in a single season, which is 28 set by Troyes Sainte-Savine in the 1960-61 campaign.
However, they have prevented themselves from breaking that record thanks to a win and a draw in their last two games.
Dujeux's side frustrated Reims in a 2-2 draw away from home, before beating fellow-relegated side Troyes 2-1 last week.
Angers are still winless in their last 14 away matches though, taking just two points in that time, and there is a strong possibility they could match the unwanted record here.
Nantes Ligue 1 form:
D
L
L
D
L
L
Nantes form (all competitions):
L
L
L
D
L
L
Angers Ligue 1 form:
L
L
L
L
D
W
Team News
Nantes will have much of their squad available for this crucial encounter on the final day.
Evann Guessand is expected to miss out after missing the last two, while backup full-back Sebastien Corchia is also sidelined.
Ludovic Blas is expected to be the difference maker for Nantes, after contributing to 11 goals already this season from the right of midfield.
Angers have been handicapped by a lengthy injury list all season, and they remain without a few first-team players for the season finale.
Nabil Bentaleb has missed the last two games and will not feature, along with Faouzi Ghoulam, Souleyman Doumbia and Amine Salama, who have all been absent for extended periods.
Ousmane Camara has already returned after France's very early exit from the Under-20s World Cup, but it is unclear whether he will be involved here.
After failing to score or assist in his first 25 appearances of the season, Himad Abdelli has found some form late in the campaign, contributing to a goal in each of his last four matches.
Nantes possible starting lineup:
Lafont; Centonze, Girotto, Castelletto, Pallois, Merlin; Blas, Pedro Chirivella, Moutoussamy, Simon; Ganago
Angers possible starting lineup:
Fofana; Thioub, Valery, Hountondji, Bamba, Sabanovic; Abdelli, Mendy, Hunou; Niane, Sima
We say: Nantes 1-1 Angers
Nantes have not looked like a side capable of avoiding the drop in recent weeks, and with their manager questioning the attitude of the players, relegation could be confirmed here.