The Toronto Globe and Mail cited government sources who said the Cabinet is expected to approve negotiations with Lockheed within a few days. The contract would be for 65 Lockheed Joint Strike Fighter F-35s, which would replace the CF-18s now in use in 2017.
The total contract would be worth up to $8.6 billion.
Boeing and other aircraft manufacturers have been lobbying for an open process, the Globe and Mail said.
"An open competition to select Canada's next-generation fighter would enable Canada's government and military to obtain access to detailed Super Hornet performance data, enabling a thorough and accurate evaluation of its advanced, proven capabilities," Boeing spokeswoman Mary Brett said.
But Prime Minister Stephen Harper and his advisers reportedly believe the only jets that would meet the requirements other than the Lockheeds would be made in China or Russia. They also say coming to an early agreement with Lockheed will fix the price of the jets.