ZURICH (Reuters) - French billionaire Bernard Arnault, Europe's richest man and the chairman of high fashion to champagne group LVMH, has bought a stake in smaller luxury rival Richemont, Bloomberg reported on Tuesday.

The exact size of the shareholding in the owner of Cartier jewellery and Arnault's intentions are unclear, the report said.

Representatives of Arnault did not immediately respond to a request for comment.

The report said the investment was small and part of a broader Arnault family-owned portfolio of investments in publicly listed companies.

Richemont, whose shares rose 2.8% after the news, declined to comment. The company's stock has gained 21% this year.

Paris-based LVMH, whose brands include Louis Vuitton and Christian Dior fashion houses, watchmakers Hublot and Tag Heuer, and champagne maker Dom Perignon, has previously bought stakes in rivals.

The world's biggest luxury company in 2010 revealed it had amassed a stake in Birkin bag maker Hermes.

Hermes' family owners reacted by binding their holdings, and LVMH eventually relinquished its stake in 2014.

Richemont could also prove a hard target to take over, if that is Arnault's intention.

The company, which also owns Swiss watchmakers IWC, Piaget and Jaeger-LeCoulture, is controlled by Chairman Johan Rupert via a combination of two categories of shares that gives him 51% of the voting rights.

Kepler Cheuvreux analyst Jon Cox said the investment seemed to be more a personal stake of the Arnault family, although he noted Bernard Arnault's admiration of Richemont's jewellery businesses.

"Arnault has made no secret that he thinks Richemont's Cartier and Van Cleef & Arpels are two world class brands and I am sure LVMH is interested and has the financial resources to do a deal," Cox said.

"However, Richemont's Johann Rupert has repeatedly said the company is not for sale and he has no interest in any sort of tie up."

Arnault in January said that Rupert was an "outstanding leader" and that he did not want to "upset his strategy."

He added: "I understand he wants to remain independent. I find that very good. If he wants support to maintain his independence, I'll be there."

Richemont last month unveiled a management overhaul, promoting Nicolas Bos, the head of its Van Cleef & Arpels jewellery brand, to become group CEO.

Still, Rupert said he was not reducing his role in the company he created.

"I'm not stepping back but I'm asking Nicolas to assume some of the direct line reporting," the 74-year-old said last month.