The Somali trainer was detained by police this week following months of investigations prompted by a tip-off from the Spanish Agency of Health and Sport (AEPSAD).
The 25 year-old Genzebe - sister of triple Olympic distance champion Tirunesh Dibaba and Olympic silver medallist Ejegayehu Dibaba - is hot favourite to win the 1,500m at this year's Rio Olympics.
"While the individual trained an Ethiopian athlete, he neither has the endorsement nor any working arrangement with the (Ethiopian Athletics) Federation," the body said in a statement on Friday.
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Ethiopia has come under scrutiny after the IAAF said it was one of five countries that were in "critical care" over their drug-testing systems.
The Horn of Africa country, which along with neighbour Kenya has for years dominated distance running on the track and the roads, subsequently announced that it would carry out doping tests on up to 200 athletes.
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