The 24-year-old has failed to turn up for training sessions since July following the expiration of his two-year contract.
He has rejected two fresh proposals, insisting on an improved deal. The Accra-based club risk losing him to an unnamed European side.
“I will not attend training without concluding contract negotiations with them," Musah was quoted as saying by Ghanaweb.
"My reason is simple and it is because it is possible the negotiation may fail and what will I do afterwards if that happens?
“The proposed contracts I have received from Hearts are two types. In one, they offered $532 per month without any signing on fee for one-and-half-a-year and the other deal also entails $3,200 for one-and-half-a-year without any further additions.
“I have also sent them my offer but since then I haven’t heard from the management of the club and even my proposed offer is not more than $4,300 per year,” he added.
Musah and his agent are expected to meet club owner Togbe Afede and chief executive officer Mark Noonan next week, according to reports.
Read Full Story