PPR chief executive Francois-Henri Pinault was speaking at a news conference at which he unveiled a new name for the luxury goods group, which will be rebranded as Kering.
Puma is 82.4 percent-controlled by PPR.
The German company, which is in the middle of an overhaul as it tries to catch up with rivals, announced the exit of CEO Franz Koch in December, less than two weeks after PPR executive Jean-Francois Palus took over as chairman of Puma's supervisory board.
There are three candidates for the CEO post, two from the sporting goods industry and one Olympian, a source familiar with the matter told Reuters on Friday.
A spokeswoman for Puma declined to comment on the hunt for a new CEO, while a PPR spokesman said: "The name of the new CEO will be announced when the contract is signed."
Koch will have held the CEO position for less than two years by the time he leaves at the end of this month.
The German company, which reported a 70 percent drop in 2012 profit, is going through its biggest reorganization in 20 years.
The management overhaul has also seen Chief Operating Officer Klaus Bauer and marketing chief Antonio Bertone agreeing to step down from their roles.
There had previously been speculation that the CEO of Danish jewellery maker Pandora (PNDORA.CO) could take the top job at Puma, but last month Bjoern Gulden issued a flat denial that he planned to move.
Reporting by Elena Berton and Joern Poltz; Editing by Dominique Vidalon and David Goodman