The former midfielder said he will be meeting with his bosses at the German club to seek permission to combine both roles.
The 46-year-old currently serves as a scout and assistant manager at Dortmund but was temporarily released to Ghana for the two-legged World Cup playoff games against Nigeria.
Addo led the Black Stars to book their place at the World Cup following a pulsating 1-1 draw against Nigeria at the Mashood Abiola Stadium in March.
A first-half strike by Thomas Partey was cancelled out by a penalty from Super Eagles captain William Troost-Ekong as both teams shared the spoils in Abuja.
The result sealed Ghana’s qualification on away goals after the first leg ended in a goalless draw at the Baba Yara Stadium in Kumasi.
Many have since called for Addo to be permanently appointed as Black Stars boss and he insists he wants to stay in the job.
“I am meeting with my bosses [Dortmund] on Thursday to discuss the Black Stars job and the possibility of continuing with them. Sure [I am willing to do Black Stars job] but I have to discuss the contract,” the interim Black Stars coach said, as quoted by 3news.
“I have a good relationship [with Dortmund] so I hope they will allow me to continue to coach the Black Stars. Hopefully [I will be able to work with Dortmund and Black Stars at the same time].”
Addo has been widely praised for turning things around very quickly, especially after the team’s disastrous campaign at the 2021 Africa Cup of Nations (AFCON).
Meanwhile, Ghana will face Portugal, Uruguay and South Korea in Group H of the Qatar 2022 World Cup.
The Black Stars will, however, first turn their attention to the 2023 AFCON qualifier, where they’ve been paired against Madagascar, Angola and the Central African Republic.