The amount covers their air tickets, accommodation and per diem for players and officials.
The Phobians, who are the only surviving Ghanaian side in Africa’s inter club competition this year, have been saddled with huge debt following their participation so far.
The club spent a combined staggering fee of $210,000 for the two-legged wins against Senegalese side Olympique Ngor as well their opening clash against AS Police of Benin.
“We will need about $40,000 for the trip to Mali. The amount will cover airfare, accommodation and per diem,” club spokesman Muheeb Saed said.
Hearts will be hoping to grind out a favourable result against the Malian side in the first leg on Friday to put them in pole position to secure qualification to the group phase.
Meanwhile,Burundi referee Thierry Nkurunziza will be in charge of Hearts of Oak’s CAF Confederation Cup game away to Djoliba this weekend.
Nkurunziza will be assisted on the lines by compatriots Jean Claude Birumushahu and Pascal Ndimunzigo in the first leg of the preliminary qualifier to be played in Bamako.
The Phobians are now Ghana’s only hope in African club competition this season following the elimination of Asante Kotoko in the Champions League by Algerian club MC El Eulma.
Hearts hope to make it through to at least the group stage of Africa’s second tier club competition.