The sources added that small parts of the third phase might be subcontracted to local firms.
There are more than 20 projects in the third phase, ranging in value from £500,000 to about £30m. Schemes include a £20m education centre and a 1000 m2 desert environment.
An Eden insider said there had been a disappointing number of bidders for the work, as many rival contractors felt that the McAlpines, which built the hugely successful first and second phases, were unbeatable.
The five-year design-and-build contract is expected to be formally awarded in the next two months.