GM's is also in constructive talks with Austria's Magna Steyr
The carmaker and Germany's economy ministry prefer a speedy agreement with Fiat, reported Spiegel Online, which has separate editorial staff from the magazine. It cited people close to the negotiations.
Fiat, Magna and Opel declined to comment.
Fiat Chairman Luca Cordero de Montezemolo last week had denied his company's interest in Opel, but media reports have repeatedly named the Italian carmaker as one of several possible strategic buyers.
GM must sell a significant stake in Opel to convince German politicians to use taxpayers' money for 3.3 billion euros ($4.30 billion) in loan guarantees.
GM Chief Executive Fritz Henderson said last week the carmaker had reached out to more than six potential buyers, many of whom were financial investors.
But private equity firms are giving Opel the cold shoulder, leaving sovereign wealth funds from the Gulf or Asia as the most interested private investors, managers at buyout firms have told Reuters.
German Bild newspaper separately said willingness was growing within German Chancellor Angela Merkel's government to grant a state guarantee if a private investor is found.
It is looking a lot better than it did four weeks ago, the top-selling German daily quoted a source in the governing coalition as saying.
Progress in talks with potential Opel investors was one of the main reasons for the more positive attitude, the paper said. Rising unit sales at the carmaker were also helping.
(Writing by Madeline Chambers in Berlin and Maria Sheahan in Frankfurt; Additional reporting by Angelika Gruber in Frankfurt, Christian Gutlederer in Vienna and Gilles Castonguay in Milan)