Lille goalkeeper Enyeama has not conceded a goal in his last 11 league outings, a run that stretches back to September 15 and encompasses 1,035 minutes of football.
Former Bordeaux keeper Gaetan Huard set the current benchmark of 1,176 minutes in the 1992-93 season, giving the Gironde club an extra incentive to find the net when Lille visit the Stade Chaban-Delmas on Sunday.
Bordeaux coach Francis Gillot has promised that any player who scores past the Nigeria international will be afforded a night out to dinner at the club's expense.
Lille's remarkable run has seen them rise to second in the table, one point behind favourites Paris Saint-Germain and one ahead of big-spending Monaco.
Victory over Marseille on Tuesday saw Rene Girard's close the gap on the defending champions, who failed to reassert their advantage a day later as they lost to Evian - a first defeat in 27 Ligue 1 games for PSG.
Avoiding a reverse would have equalled PSG's club-record unbeaten league run, but they will be confident of atoning for the loss when they host rock-bottom Sochaux on Saturday, while Monaco will also be heavy favourites against Ajaccio, who are second from bottom.
Nantes have surprised many after their promotion back to France's top flight following a four-year absence and go into the weekend fifth.
Michel Der Zakarian's side face a tough test to prove their lofty position is merited when they travel to Marseille - a point and a place above them - on Friday.
Marseille had won three games in a row prior to their Lille loss, while Nantes were on a four-match unbeaten run on their travels before surprisingly losing at Guingamp last week.
The Breton outfit responded with a 2-1 home success over Valenciennes in midweek, although they have lost to the other three teams above them in the table already this season.
Another game with a distinctly Breton flavour sees local rivals Lorient and Rennes face off at the Stade du Moustoir.
Elsewhere, Evian will hope to build on their humbling of PSG at Saint-Etienne and Lyon will once again look to kickstart a floundering season at Bastia - unbeaten in four.
Southern rivals Toulouse and Montpellier meet at the Stade Municipal, Guingamp travel to Valenciennes, and Reims host Nice.
