Adamu was suspended for three years in November following claims he had asked for money in exchange for his World Cup vote.
The Confederation of African Football (Caf) revealed both Africa's outgoing members - Adamu and Jacques Anouma - are reapplying for their posts.
Adamu's position is up for re-election next month.
Should Adamu, who has protested his innocence, fail in his appeal to Fifa against his suspension, compatriot Ibrahima Galadima will be applying on behalf of Nigeria.
Other applicants for the posts include Zambia's 1988 African Footballer of the Year Kalusha Bwalya and South African Danny Jordaan, who earned widespread praise for his role as CEO of the 2010 World Cup organising committee.
Making up the list are Algerian Football Federation president Mohamed Raouraoua and Suketu Patel, who heads up the Seychellois federation.
Caf is set to elect its members at a general assembly in the Sudanese capital Khartoum on 23 February.
With regard to the African body itself, six positions on the executive committee are being contested by a total of 16 men across the continent.
Two of those aiming for a place on the Fifa executive, Bwalya and Jordaan, are aiming to replace outgoing member Dr Molefi Oliphant as he vacates his position in Southern Africa.
Elections for Caf's Executive Committee (to cover 2011-2015):
Outgoing Member: Hani Aboo Rida (Egypt)
Candidates: Hani Aboo Rida, Tarek Bouchamaoui (Tunisia)
Zone West A
Outgoing Member: Almamy Kabele Camara (Guinea)
Candidate: Almamy K. Camara
Zone West B
Outgoing Member: General Seyi Memene (Togo)
Candidates: Anjorin Moucharafou (Benin), Kwesi Nyantakyi (Ghana), Tata Adaglo Avlessi (Togo), Hima Souley (Niger)
Outgoing Member: Thierry Kamach (Central African Republic)
Candidate: Omari Constant (DR Congo)
Outgoing Member: Célestin Musabyimana (Rwanda)
Candidates: Célestin Musabyimana, Leodegar Tenga (Tanzania)
Outgoing member: Molefi Oliphant (South Africa)
Candidates: Adam Mthethwa (Swaziland), Kalusha Bwalya (Zambia), Danny Jordaan (South Africa), Walter Nyamilandu (Malawi), John Muinjo (Namibia), Justino Fernandes (Angola)