The Daily Telegraph newspaper said the next contract to produce British passports would be awarded to Gemalto, while the head of UK manufacturer De La Rue said he had been told his company had lost out to the Franco-Dutch firm.
De La Rue boss Martin Sutherland said it was "disappointing and surprising" that "this icon of British identity" would be manufactured by a foreign company.
"We've had that confirmed to us by the Home Office," he told BBC radio in reference to Britain's interior ministry, though the government said the process had not concluded.
Sutherland said he wanted to invite British Prime Minister Theresa May to his factory and explain "why they think this is a sensible decision to offshore the manufacture of a British icon".
An interior ministry spokesman said the preferred bidder had been "selected following a rigorous, fair and open competition".
"It's been the case since 2009 that we do not require passports to be manufactured in the UK," they added.
The ministry said the new contract will save the taxpayer approximately £120 million ($160 million, 137 million euros) and will lead to the creation of up to 70 jobs.
"The preferred supplier is an experienced and trusted company which already work with the government on the production of UK driving licenses, UK Biometric Residence Permit cards and on e-gates at the border," it added.
'National humiliation'
Priti Patel, a figurehead of the pro-Brexit campaign in Britain's 2016 referendum vote to leave the EU, said: "The return of our iconic blue passport will re-establish the British identity.
"But to be putting the job in the hands of the French is simply astonishing. It is a national humiliation," the former cabinet minister told The Sun newspaper.
The return of blue British passports in place of standard burgundy European Union ones is seen as a hugely symbolic reclamation of UK sovereignty for those backing Britain's exit from the bloc.
UK passports had dark blue covers from 1921. But Britain switched to burgundy from 1988, in common with other passports of what was then the European Community.
Britain is set to leave the EU in March 2019. The new passport production contract starts in October 2019.
The Best for Britain campaign group, which wants to keep the door to EU membership open, hit out at Brexit supporters unhappy at passports being produced by a foreign company.
"All these Brexiteers claim to be champions of global free trade until it doesn't work out for their interests -- at which point they magically transform into angry isolationists who don't back British firms to compete around the world," a spokesman said.
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