Iraq has been among the countries most affected by the Hormuz shutdown.
It exported around 3.6 million barrels of oil per day before the war, mainly through Gulf terminals near Basra, but shipped just 35.5 million barrels in total via Hormuz in July, according to state-run oil firm SOMO.
A pipeline linking Iraq's northern Kirkuk region to Syria's Mediterranean port of Banias already exists but was badly damaged by wars in Iraq and Syria and has not been in regular use since the 1980s.
Both sources said the plan would require laying entirely new infrastructure rather than rehabilitating the existing pipeline and cost at least $15 billion.
While part of the new pipeline would run largely along the same Kirkuk-Banias route, intact sections of that pipeline are not compatible with newly developed specifications and would be unusable, one of the sources said.
The second source said the project would include developing an entirely new integrated crude oil pipeline system that would link Iraq's southern and northern fields to a central hub in Haditha in western Iraq, then onwards to Banias.
The U.S. has welcomed the "rehabilitation and reconstruction" of the pipeline, saying it will have initial transport capacity of 2 million bpd of crude oil.
That would imply a major expansion of the old pipeline's capacity of about 300,000 bpd, which is less than a tenth of the oil volume Iraq exported through the Strait of Hormuz before the Iran war.
Iraq has also restarted oil exports from its Kirkuk fields via pipeline to Turkey's Ceyhan port with targeted capacity of around 250,000 bpd.
Both sources said work on the Iraq-Syria pipeline would take around four years, though one added that the timeline may also need to accommodate clearing old infrastructure and acquiring fresh land use rights from Syria's new administration.
Syria and Iraq have both signed separate memorandums of understanding with a consortium comprised of U.S. major Chevron, TI Capital and Qatar's UCC Holding to carry out technical and financial studies in preparation for the project.
Iraq's oil ministry and state-owned Syrian Petroleum Company did not respond to Reuters requests for comment on the project and the sources' timeline and cost assessments.
TI Capital and UCC Holding did not immediately respond to requests for comment. Chevron pointed to an earlier statement about the preliminary agreement and said it does not comment on details related to commercial matters.
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