Family-controlled Berge intends to raise cash from the operation to expand Astara, a network of car dealerships in 19 countries in Europe, Latin America and Asia, Expansion said.
The operation could value the company at around 2 billion euros ($2.09 billion), the newspaper said.
Berge, Astara, BNP Paribas, Morgan Stanley and HSBC did not immediately respond to request for comment.
After a drought of new listings on the Madrid stock market in the last few years, several companies in industries ranging from airlines to luxury and tourism were reportedly weighing initial public offerings over the past few weeks.
($1 = 0.9556 euros)
(Reporting by Inti Landauro, Editing by Louise Heavens)