The Under-20 World Cup winning coach arrived in Kigali on Tuesday night before heading into discussions with his representative on Wednesday.
Both Tetteh and Rwanda's sports authorities are keen on a deal and an announcement could be made as early as Thursday evening announcing the Ghanaian as the new boss of the Amavubi.
The permanent secretary in the Ministry of Sport, Mr Jean Pierre Karabaranga is confident that an agreement will be in place by Thursday.
"He knows Rwandan football and he likes the country, so we'd be happy to get him to train our team," he said.
Tetteh has built up his reputation strongly over the last four years, serving as assistant coach for Ghana at the 2006 World Cup and the 2008 Nations Cups. He then took charge of the Black Stars after the 2008 Nations Cup helping the team reach the second stage of the qualifiers with four victories out of five games before the Serbian Milovan Rajevac took over.
Last year in Kigali, he masterminded a thrilling Ghana victory at the African Youth Championships and followed up by guiding the Black Satellites to become the first African winners of the Fifa Under-20 World Cup.