On January 3, the GFA confirmed that Kwesi Appiah, his technical team and all coaches at all age-group levels of football had been relieved of their duties.
Within the restructuring of their football federation, Cuper, who led Egypt to the 2018 FIFA World Cup has put his name in the hat for the job.
According to Ghana Football Web, Cuper's agent Alejandro Camano claimed the 64-year-old is attracted to the challenge of leading the Black Stars.
"Ghana is a strong team and a great country that can undertake a huge project and achieve many glories," Camano said.
"Mr Cuper is full of ambitions and dreams. He is always working like that and lives the dream of every nation as he did in Egypt.
"Mr Cuper also likes the slogan of the new President of the Ghana FA #BringBackTheLove."
Despite the recent upheaval at boardroom level, Ghana currently lead their 2021 Africa Cup of Nations qualifying group C with six points, three ahead of second-placed Bafana Bafana.