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The Super Eagles, who won the competition in 2013, are currently bottom of Group A after a shock 1-0 defeat away to Sudan and just a single point from three games in the qualifiers.
Nigeria host Sudan, who are now third in the standings with three points, in a return fixture on Wednesday in the capital, Abuja.
Next month, they travel to second-placed Congo, who defeated them 3-2 in September, before the arrival of group leaders South Africa.
Nigeria have to win all three matches and hope other results go their way if they are to stand any chance of qualifying for the finals in Morocco in January.
Keshi, whose position has been the subject of repeated speculation, has apologised for the defeat to Sudan but at the same time claimed there was a conspiracy to ensure that he fails.
"There is a sabotage by some people. I won't mention their names but they know themselves. They want to run this team down," he claimed.
"Some people are ready to sell this country for a dime. They want to sabotage the Super Eagles.
"It's a shame. They don't want this team to get to the AFCON (Nations Cup), they want this team to lose outright. But they are not God.
"And this is not Keshi's team. Keshi is a professional coach and after this (assignment), he will get another job elsewhere."
Nigeria fans awaiting the team's return from Sudan at Abuja airport on Sunday roundly booed the players and question marks about Keshi's future dominated the country's media on Monday.
The 52-year-old does not have a contract with the Nigeria Football Federation (NFF) after his initial three-year deal ran out following the World Cup finals in Brazil.
He led Nigeria to win a third Nations Cup last year and guided the Eagles to reach the World Cup knockout stage.
But he has lost the support of many players after much-publicised rows with the likes of Emmanuel Emenike, Peter Odemwingie and Ikechukwu Uche.
His record of five defeats, five draws and just one victory in the last 11 matches has only compounded dissatisfaction.
"The boys did not play for their coach (against Sudan) and he (Keshi) should now know what to do," said Larry Izamoje, owner of Nigeria's all-sports radio Brila FM.
Most fans have equally demanded for the dismissal of the coach.
One Nigeria supporter in Lagos, Mike Johnson, said Keshi has nothing more to offer.
"After watching Eagles against Congo and South Africa, I concluded that Eagles are going down," he said.
"But when I watched them against Sudan, I know that is the end of Keshi era because I saw no touch of technical input in the team.
"The performance of the team was an eyesore. Keshi should be sent away."
The NFF's new president Amaju Pinnick also criticised the defeat in Khartoum but maintained that they will not rush a decision over Keshi's future and would act in the country's best interest.
"It is embarrassing that as reigning champions, we are struggling in the qualifying series, with only one point out of a possible nine. It is an awful output," he said.
"However, we want our people to be patient and not stampede the federation to take knee-jerk decisions that will backfire in the end.
