PSA Group has scheduled a press conference with GM for Monday morning in Paris.
The two companies had wanted to announce a deal before the start of the Geneva motor show on Tuesday.
The sale could threaten the jobs of 4,500 workers at Vauxhall's plants at Ellesmere Port and Luton.
Union officials said on Sunday that Vauxhall staff had endured a "nerve-wracking" few weeks.
Buying GM's loss-making European operations will make PSA the continent's second-biggest car maker after Volkswagen and ahead of French rival Renault.
PSA and GM Europe sold a combined 4.3 million vehicles last year and posted revenues of 71.6bn euros (Â£61.9bn).
The two companies already share some production and confirmed last month they were in talks.
Opel had hoped to return to profitability by 2016, but the slide in sterling following the EU referendum last June contributed to its 257m euros annual loss.
In contrast, Ford Europe managed to make a pre-tax profit last year despite the pound's collapse.
Opel has failed to emulate Ford or PSA in reducing overcapacity at its factories, despite closing a plant in the western German city of Bochum with the loss of 3,000 jobs in 2014.
Stefan Bratzel, of Germany's Center of Automotive Management, said: "Opel suffers more from overcapacity than other European carmakers, meaning it has to offer big discounts to keep up a certain level of production and that hits its profitability."
In a bid to protect its Buick and Chevrolet brands, GM has not allowed Opel to expand outside Europe.
"All the western carmakers have been making their money in the Chinese market these past few years," said Marc Staudenmayer of the Advancy management consultancy.
"Opel wasn't allowed to do that, which explains its underperformance since 2005. Opel was reined in too much by GM," he added.
GM's European operations have lost money for 16 consecutive years and were almost sold in 2009.
For PSA, the deal caps a stellar two-year recovery under chief executive Carlos Tavares, who is expected to slash costs at Opel in a bid to generate savings of up to 2bn euros a year.
Jim Holder, of What Car? magazine, told the BBC: "PSA has capacity to build more cars in its own plants - it doesn't need these plants in Britain.
"And of course there are obstacles in the way, with the currency fluctuations, the problems posed by Brexit with freedom of movement, freedom of movement for parts as well."
Len McCluskey, general secretary of the Unite trade union, said he had spoken to the chief executives of GM and the PSA Group over the weekend.
"While initial discussions with the PSA Group have been relatively positive, our priority now is to ensure a long-term future for our plants and the tens of thousands of workers depending on them," Mr McCluskey added.
Greg Clark, the Business Secretary, said last month that Vauxhall workers had no reason to fear for their jobs.
"We have a very strong domestic market and Vauxhall has a large share of that - something PSA recognises," he told MPs.
"From my initial conversations I think it is understood that Vauxhall's plants are very efficient."
Mr Tavares recently told analysts the acquisition offered an "opportunity to create a European car champion" and quickly exceed five million sales annually.
PSA also plans to revamp Opel's model range. "There are market segments where Opel isn't very strong, like SUVs," Mr Staudenmayer said.
General Motors is set to announce a deal to sell its Vauxhall and Opel operations to the French company that owns Peugeot and Citroen.