The Phobians are currently without a substantive head coach following the acrimonious departure of Martin Koopman last month.
Assistant coach Abdul Rahim Bashiru has since been promoted to the role of interim manager as the hierarchy of the club hunts for a substantive boss.
Speaking on the club’s search for a new head coach, Sowah Odotei said they were targeting a coach with the pedigree of Mosimane, although financial constraints are proving to be a stumbling block.
“Those of us in charge of Hearts of Oak now, we want to bring someone like Pitso Mosimane. Can we afford him? Do you know how much he was being paid at Al Ahly?” the board member told Asempa FM, as quoted by Joy Sports.
“The point I am trying to make is that, when appointing a coach, a lot of considerations come into play.
“If the fans are patient with us a bit, we believe we will get to a stage where we can attract world-class coaches.”
South African coach Mosimane is one of the most successful managers on the continent, having won major trophies wherever he has been.
The 59-year-old won five league titles with Mamelodi Sundowns, the CAF Champions League and CAF Super Cup.
At Al Ahly, he guided the club to win two Champions League titles, the Egyptian Cup and finished third in the FIFA Club World Cup twice.
Mosimane, who was also named CAF Coach of the Year in 2018, is currently unattached after parting ways with Abu Dhabi side Al Wahda in November.