The daily cited "two people close to the matter" for its information but said Ripplewood could not immediately be contacted for comment.
Opel declined to comment on the report, the newspaper added.
Ripplewood Holdings, a New York-based private equity fund, already controls German auto components maker Honsel.
The German government is looking to secure Opel's future by finding a buyer to take it from General Motors, which said Monday that it faced the increasing likelihood of having to file for bankruptcy.
Italian automaker Fiat, teaming up with already bankrupt Chrysler, has said it is ready to take on GM's European assets, including Opel, which directly employs 26,000 people in Germany.
Meanwhile Canadian auto components manufacturer Magna, linked to Russian vehicle company GAZ, might also be interested in Opel.
Financial daily Handelsblatt reported Wednesday that Magna could unveil an offer for Opel as early as this week, backed by Russian lender Sberbank which could take more than the 30 percent stake it first envisaged in the GM unit.