Congo need just a point to qualify for the knockout stages for the first time since in 23 years, while only a victory will do for 2013 finalists Burkina Faso in the final group match.
Prince Oniangue scored the solitary goal against Gabon on Wednesday to send Congo top of the group and on the brink of progressing to the quarter-finals.
It has been 15 years since Congo - the 1972 champions - qualified for the AFCON and the experienced Le Roy is determined to ensure their tournament is not cut short.
He said: "I am a coach that hates draws. I will never prepare my team to go for a draw. We are going to play for a win against Burkina Faso.”
While Congo's players lack the experience of playing in the prestigious tournament, French coach Le Roy is in his eighth Cup of Nations and the 66-year-old is loving every minute of his latest challenge.
"It's unbelievable," said Le Roy. "We were in the same [qualifying] group as Nigeria. We created a huge surprise in Calabar [beating defending champions Nigeria 3-2]. But with this team, anything is possible. They like to work, they like to sing together."
Although Congo stand on the brink of reaching the quarter-finals, Le Roy is not getting ahead of himself.
He added: "The final? Please, the final is a long way off. We are talking about getting to the last eight first."
Burkina Faso have not yet scored a goal in the tournament, having lost 2-0 to Gabon in their first game before being held to a goalless draw by hosts Equatorial Guinea.
Even a victory may not be enough for Paul Put's men to avoid an early exit, much to the dismay of captain Charles Kabore.
He said: "Our fate now would depend on the outcome of the match between Gabon and Congo. We no longer have our destiny in our hands in this competition. It’s so sad."
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