Struggling U.S. carmaker General Motors Corp
Armin Schild, who represents labor union IG Metall on the board, told Reuters Fiat was in talks with GM to buy a controlling interest in Opel.
Earlier German magazine Spiegel Online had said that Fiat would sign a letter of intent next Tuesday, citing people close to the negotiations.
However, Fiat declined to comment and a spokesman for Opel reiterated that the company was in talks with several interested parties, declining to say who these parties are.
Schild said IG Metall strictly opposed such a deal with Fiat for fear that the Italian rival would only try to prop up its own business rather than help rescue Opel's business.
Opel cannot survive with two sick parents and a Fiat deal would lead to less autonomy for an Opel Europe rather than more, Schild said.
Fiat is also in partnership talks with another troubled U.S. group, Chrysler LLC
The Italian company faces an April 30 deadline to win the support of Chrysler's creditors and unions, and some analysts have said it could turn to GM to gain the scale it needs to survive the worst industry crisis in decades.
Fiat's Chief Executive Sergio Marchionne has said a car maker needs to make more than 5 million vehicles a year to make a profit in this new tough automotive world.
If he wants to do 5.5 million vehicles and Chrysler doesn't work out he will need to find another Chrysler, Morgan Stanley analyst Adam Jonas said.
GM needs to sell a big stake in Opel to get 3.3 billion euros ($4.30 billion) in loan guarantees from Germany and other European governments to rescue the troubled unit.
Opel employs about 25,000 people in Germany, where the government is five months away from elections.
Spiegel Online said GM was also in talks with Canadian autoparts maker Magna
Fiat's chairman, Luca Cordero de Montezemolo, denied last week having any interest in Opel, despite a growing number of press reports citing the Italian car maker as a possible buyer.
Shares in GM were down 1.2 percent at $1.67 at 1347 GMT (9:47 a.m. EDT). Shares in Fiat, which reported a first-quarter loss but confirmed its targets for the year earlier on Thursday, were up 1.3 percent at 7.57 euros in Milan.
In its statement on the results Fiat said it would keep pursuing its strategy of targeted alliances while conducting talks with Chrysler.
The big question about the Opel case is where do they (Fiat) find the resources (to buy a stake and help turn it around)? asked a Milan analyst.
Fiat also faces doubts about its ability to pay off 4.8 billion euros of debt this year.
(Additional reporting by Madeline Chambers in Berlin, Angelika Gruber in Frankfurt and Christian Gutlederer in Vienna; Editing by Andrew Callus)