Senegal have already been eliminated, while Libya want to win this Africa Cup of Nations Group A match on Sunday to boost their chances of advancing to the knockout stage.
Pre-tournament Group A favourites Senegal were the first major casualty to crash out of the Nations Cup after they lost their first two matches to Zambia and co-hosts Equatorial Guinea.
Libya, on the other hand, kept alive their hopes after they drew 2-2 with Zambia following a 1-0 loss to home team Equatorial Guinea in the opening match of the competition.
The North Africans could now make it into the quarter-finals along with Equatorial Guinea if they win well against Senegal and the co-hosts do them a big favour and also beat second-placed Zambia, who are on four points from two matches.
"We still have a chance to qualify, but it partly depends on the outcome of the other game (Equatorial Guinea against Zambia)," said Libya coach Marcos Paqueta.
"Senegal are a good team, but we want to fight and win and stay in this tournament."
Libya reached the final of the championship when they hosted it in 1982, but in subsequent participations they have failed to go past the first round.
However, for a country that has been ravaged by a civil war, which forced the Confederation of African Football (CAF) to withdraw their hosting rights for the 2013 edition of the competition, they have done well so far.
They lost by one goal to an inspired Equatorial Guinea in their first game, where they played with some caution.
They were a lot more daring against Zambia only to be forced to a 2-2 draw under terrible conditions caused by a tropical rain storm that delayed the match kick-off by an hour and made the pitch water logged and almost unplayable.
For the Teranga Lions from Senegal, they want to exit this championship with their heads held high after a rather disappointing showing.
Their pride has again been hurt after they were kicked out in the first round as was the case at the 2008 Nations Cup in Ghana.
The team's premature exit has been described as a national disgrace and they can no longer look forward to a 30,000 euros bonus and a house, promised to each player by the country's President Abdoulaye Wade if they won the competition.
"We will prepare very seriously for the match against Libya and play with honour till the end," vowed captain Mamadou Niang, one of several of Senegal?s top strikers who have failed to find the back of the net so far.
"We have been unlucky and also we are a young team with most of the players here for the very first time.
"This disappointment can only make us grow and make progress."
Senegal will now turn their attention to the qualifying campaign for the 2014 World Cup, which starts in June and they are drawn against Uganda, Angola and Liberia in the first league phase.