The crude would be transported to the Kenyan coast, a senior Kenyan energy official said on Wednesday.
Uganda and Kenya have discovered commercial quantities of oil and aim to start production in the next three years or so.
Their neighbour, South Sudan, is a producer that now relies on a pipeline through Sudan but ties between those two states have been strained since they split from each other in 2011.
"What we want is to procure one supervisor for the entire pipeline so that the quality of the pipeline is the same," Joseph Njoroge, the Energy and Petroleum Ministry's principal secretary, told reporters.
"In two to three weeks we should see the advertisement for the consultant," he said on the sidelines of a meeting to discuss his ministry's five-year strategy to 2017.
East Africa has become hot property for international oil firms after Kenya and Uganda's commercial oil finds and discoveries of gas off the coast of Tanzania and Mozambique.
Tullow Oil and Africa Oil, which control blocks in Kenya, have estimated discoveries in the South Lokichar basin at 600 million barrels, a level experts say is enough to make a pipeline viable even without Uganda.