Much-travelled Daum who coached several teams in the German Bundesliga as well as clubs in Turkey, Austria and Belgium, refused to talk to reporters about his potential appointment but local media reported that the 62-year-old had already reached an agreement with the Romanian Football federation (FRF).
The FRF will officially announce the new coach on Thursday.
FRF president Razvan Burleanu said on Sunday that a foreigner would replace Anghel Iordanescu who stepped down after Romania's failure to make it past the European Championship group stages.
Daum is expected to become only the second foreign coach of Romania after Austrian Josef Uridil, who led the team at the World Cup in 1934.
If appointed, Daum will have the task of leading Romania to the 2018 World Cup finals in Russia. The Tricolours have been drawn in qualifying Group E alongside Denmark, Poland, Montenegro, Armenia and Kazakhstan.
(Reporting by Angel Krasimirov; editing by Martyn Herman)
