Abubakar is currently unattached after he was sacked by the Fire club on Tuesday.
GHANAsoccernet.com sleuth hounding indicates the soft-spoken gaffer has held initial talks with Hearts over the possibility of taking up the job.
Abubakar has consistently been linked with a move to Hearts in the past two-years and appears he will get his dream job.
He guided the team to clinch the Ghana Premier League crown last season but the side's unflattering campaign this term has not helped his reputation.
The Phobians are without a substantive coach after Henry Wellington was sacked last month.
Seth Hoffman has been appointed in a stop-gap role but will revert to an assistant if Abubakar finally signs for the club.
The suspension of the Ghanaian top-flight will be viewed as an ideal time to begin the transition.