Hearts are keen to tie down the rugged centre-back but their failure to meet his asking price has stalled negotiations.
Boampong played a commanding role for Hearts last term until he was knocked down by an injury which kept him out of action in the latter stages of the campaign.
Reports have emerged that the 21-year-old is not keen on renewing his contract with the capital-based side but rather relishing the prospect of playing pursuing a dream move abroad.
Hearts have been unusually slow in the transfer-market this term and the likely departure of the former Berekum Arsenal player will be a massive blow to coach CK Akunnor and his backroom staff.
Boampong was member of Ghana’s Under-20 side that won the Fifa U-20 World Championship in Egypt.
He is the younger brother of former Hearts defender Dan Coleman and joined the Phobians in 2009.