The plan was unveiled during a meeting of BMA executives on Monday morning, a source at the meeting said.
The plan is in addition to an ongoing project by the Metropolitan Electricity Authority to bury power cables.
The source said the meeting agreed to hire an advisory firm to draft a master plan for the project, which will be carried out in seven phases over five years.
Bidding for the advisory firm will be opened at the BMA-owned Bangkok Thanakhom Co Ltd on February 16.
In the first phase, the bid winner will spend five months drafting a master plan. In the second phase, the BMA will seek a joint venture and in the third phase, it will open bidding for construction.
The construction was supposed to start in the second year, the source said.
According to the BMA, there are 5,097 roads and sois in Bankgok with a total distance of 3,515km. They include 87 main roads spanning 976km, 223 subsidiary roads for 1,204km and 103 minor roads for 520km. It was unclear what routes accounted for the additional 815km.