France thrilled in their first two group games, beating Honduras 3-0 and crushing Switzerland 5-2, and although a much-changed side then drew 0-0 with Ecuador, they find themselves being discussed as potential champions.
However, Deschamps has told his squad not to start looking beyond Monday's tie at Brasilia's Mane Garrincha National Stadium and he batted away questions about France's chances of winning the tournament in his pre-game press conference.
"My only concern is Nigeria in the last 16 and to make sure with my staff that we prepare the players for battle tomorrow (Monday)," he said.
"There's no point looking beyond that. Our rendezvous is tomorrow at one o'clock (1600 GMT).
"It's not like the group phase, where you can make amends. The verdict falls at the end of the match. It's a cup configuration, it's the second phase of the competition.
"We prepare for the matches with the same seriousness, but at the end, either you stay or you go home."
Centre-back Mamadou Sakho is a major doubt for France after a thigh injury forced him to train apart from the rest of the squad for the second day in succession on Sunday.
Yohan Cabaye is due to come into the team in place of Morgan Schneiderlin after missing the Ecuador game at the Maracana through suspension, but Paul Pogba's place is under threat from Moussa Sissoko.
- Bonus row -
Having been rested against Ecuador, Mathieu Valbuena is also in line to return, while Deschamps must choose between Antoine Griezmann and Olivier Giroud to complete France's front line alongside three-goal Karim Benzema.
Moses could come into the team in place of Michel Babatunde, who fractured his wrist in Wednesday's 3-2 loss to Argentina, which would oblige Peter Odemwingie to take up a central role at the tip of the Nigerian midfield.
Nigeria's preparations for the game were disrupted by a row over bonuses that saw the squad refuse to train on Thursday, but both coach Stephen Keshi and midfielder John Mikel Obi played the matter down on Sunday.
Keshi, who led his side to victory in last year's Africa Cup of Nations, says that he is eager to pit his players against Deschamps's exciting, emerging France.
"It doesn't surprise me that France have a very good team, with players who play for big clubs," he told his pre-game media conference.
"They've started well and they're playing well. Didier knows what he wants. He's a fighter, and he's always had that in him.
"He's a great professional and he's remained so by becoming a coach and constructing a great team."
It will be Nigeria's first World Cup knockout match since the 1998 tournament in France and victory would see the West African nation reach the quarter-finals for the first time in their history.
The sides have met only once before, in a friendly match in Saint-Etienne in June 2009 that saw Nigeria emerge with a 1-0 victory.
France have also suffered damaging defeats to African teams at two of the previous three World Cups, crashing 1-0 to Senegal as holders in 2002 and going down 2-1 to hosts South Africa in their fateful 2010 campaign.
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