Parly personally took the decision to drop the bilateral meeting with British Defence Secretary Ben Wallace, the sources said.
The French defence ministry could not be immediately reached. The British defence ministry declined comment.
The sources confirmed an earlier report in the Guardian newspaper that the meeting had been cancelled.
The scrapping of the multi-billion-dollar submarine contract, struck in 2016, has triggered a diplomatic crisis, with Paris recalling its ambassadors from Washington and Canberra.
France claims not to have been consulted by its allies, while Australia says it had made clear to Paris for months its concerns over the contract.
French President Emmanuel Macron and U.S. President Joe Biden will speak by telephone in the coming days to discuss the crisis, the French government's spokesman said on Sunday.
