The ambitious project has been in the works for more than a decade and aims to provide much-needed water to Jordan, Israel and the Palestinian territories.
It moved closer to reality in December 2013 when Israel, Jordan and the Palestinian Authority signed a water-sharing deal.
In February, Israel and Jordan took a further step by signing an agreement to build a pipeline linking the Red Sea to the Dead Sea.
Experts have warned that the Dead Sea, the lowest and saltiest body of water in the world, is on course to dry out by 2050.
Its degradation started in the 1960s when Israel, Jordan and Syria began to divert water from the Jordan River, the main source for the Dead Sea.
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On Tuesday, Jordan's water and irrigation ministry invited private companies and consortiums to submit prequalification documents for the development and execution of the project's first phase by March 30, 2016.
The submission of such documents is a standard first step in procuring contracts for civil works.
The first phase of the project -- with an estimated cost of $900 million -- involves building a conveyance system to transfer 300 million cubic metres of water each year from the Red Sea to the Dead Sea.
Some of the water pumped from the Red Sea would enter the Dead Sea while the rest would be desalinated and shared with Israel and the Palestinian Authority.
The ministry said the project would later include building desalinated water pipelines, a seawater desalination facility and a hydroelectric power generation facility.
Water is a rare resource in Jordan, where 92 percent of the land is desert. The country is home to around seven million people and the population is growing with an influx of refugees from Syria.
Several environmental groups have warned that the project could undermine the fragile ecosystem of the Dead Sea, which they fear could be contaminated by water from the Red Sea.