Elimina Sharks has only won one of their last seven matches between Hearts of Oak and drew three out of the seven matches.
Hearts of Oak also want to continue with their successful season by winning double.
Ashgold will also host Kintampo Top at Obuasi while Kumasi Asanti Kotoko host Berekum Chelsea.
See the full draw below;
🇬🇭 Ghana MTN FA Cup Quater Final draw
Ashgold 🆚 Kintampo Top
Kotoko 🆚 Berekum Chelsea
Elmina Sharks 🆚 Hearts of Oak
Medeama 🆚 Attram De Visser