Sofapaka believe they can overcome a three goal defecit against Tunisian visitors Club Africain on Sunday and reach the Confederation Cup group phase.
The Kenyan side have already staged a second-leg recovery in the tournament as they beat former African champions Ismaili from Egypt in an earlier round.
Having lost 3-0 in the first leg they, need to win by the same scoreline to take the fourth-round tie to penalties.
If the Tunisians score once Sofapaka would need five goals to survive.
Sofapaka have already created history by becoming the first Kenyan team to make the last 16 of the second-tier African club competition.
"When we started out no one believed we could make it to this level. Every hurdle we have overcome has been a success for us," says coach Francis Kimanzi.
"It is a tall order to overcome Club Africain, but not an impossible one.
"The Tunisians do not intimidate us tactically or technically. The first leg result was not a true indication of their superiority."
Captain James Situma backs his boss: "Nothing is impossible and hopefully we can produce another stunning victory like we did against Ismaili."
Khaled Melliti was the architect of the 3-0 first leg triumph with a goal early in each half for Club Africain, who also changed coaches recently with former national team boss Faouzi Benzarti replacing Kais Yacoubi.
Simba of Tanzania are the other contenders from the east of the continent and have home advantage on Sunday over troubled Daring Club Motema Pembe from the DR Congo in a delayed first leg.
Kinshasa-based Pembe sacked Belgian coach Nasreddine Nabi this week because of poor domestic results and his alleged inability to work with two assistants, one of whom has been put in charge for the Dar es Salaam fixture.
Nigeria could have two clubs among the last eight with, Kaduna United needing to overcome 1-0 away loss against Entente Setif of Algeria and Sunshine Stars hosting Al Ittihad in tie reduced to one leg because of the Libyan conflict.
Asec Mimosas of Ivory Coast appear certain to reach the group stage after easily beating Primeiro de Agosto of Angola 4-0 in Abidjan.
JS Kabylie of Algeria - one of four former African champions in the field - are another team set to progress having forced a 1-1 draw with Diaraf in Senegal, despite being severely weakened by injuries and suspensions.
Morocco have already lost one of three challengers, after the elimination of holders FUS Rabat.
And their counterparts Difaa al-Jadida are in trouble having fallen 3-0 to InterClube in Angola, while MAS trail Zambian visitors Zesco United by one goal.