Initial reports are that Akono and his assistants will be in charge for the vital World Cup qualifiers against Togo on 9 June and DR Congo a week later, as well a friendly against Ukraine before that.
However with Akono still recovering from a suspected mild heart attack over the weekend Finke may start his role sooner than expected.
It is understood that fromer France boss Raymond Domenech and Antoine Kambouare were also considered for the job.
Frenchman Domenech, 61, was manager of his country's national team between 2004 and 2010, taking them to the runners-up spot at the 2006 World Cup finals.
However, he has no experience of African football at either club or national level and has not been involved in football management since the end of his time in charge of Les Bleus.
Kambouare is also a free agent, having been sacked by Saudi Arabian side Al Hilal FC in January this year.
The former Paris Saint Germain manager, 49, also has no coaching experience in Africa.
Meanwhile, Fecafoot has contacted the 25 members of the squad named by Akono for the upcoming World Cup qualifiers, as well as the friendly against Ukraine on 2 June.
After Akono circulated details of the squad, Fecafoot stated it had rejected his selections because it expected to have a new man in place who would make his own selections.
BBC Sport has been told that Akono's squad has now been accepted.