Len McCluskey, the Unite union leader, said he welcomed a "positive" meeting with the UK's business secretary about the tie-up, saying he had "responded to our call that the government needs to be involved".
The French government, which owns 14% of PSA, could support a deal that would help PSA reach critical mass, an economy ministry source said.
GM is reportedly seeking a multi-billion dollar amount for Opel.
Detroit-based GM has been trying to return its European business to profit. Selling to PSA is a lower risk in that sense because the two companies already share some engine and chassis technology.
Combining PSA Group with Opel and its British brand Vauxhall would create the second-largest carmaker by market share in Europe, with 16.6 percent of sales according to 2016 figures. It means the biggest auto industry merger or takeover since Fiat bought Chrysler at a knock-down price from the USA government in the wake of the global recession, and it's likely to trigger a major round of mergers and acquisitions in the vehicle world, with smaller brands vulnerable to buyout.
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Together, PSA and Opel would command a 16.3 percent share of the European auto market share compared with Volkswagen's 24.1 percent, based on 2016 data.
Germany's IG Metall labor union and Opel's works council said they were caught by surprise with news of the potential sale of Opel to PSA, the maker of Peugeot and Citroen brand cars.
The Vauxhall brand, purchased by General Motors in 1925, presently accounts for around one-fifth of Opel sales, with the United Kingdom traditionally being the largest market for the Corsa and Insignia.
In recent years, GM sought to increase its co-operation with Peugeot and Citroen, in an effort to cut manufacturing costs and improve the profitability of both Opel and Vauxhall. "We like the deal, particularly from General Motors' perspective". In a life-saving measure, the Peugeot family was forced to sell 25.6 per cent of its stake in the French vehicle maker, with 12.8 per cent going to the French government and a further 12.8 per cent to Peugeot's Chinese joint venture partner Dongfeng. However, a devaluation of the British pound and cooling sales in the United Kingdom following the Brexit vote is claimed to have resulted in an added $300 million of unexpected currency losses in 2016, leading to an operating loss at Opel of $257 million past year.