China may soon cinch another knot in its business ties with Malaysia.

Zhejiang Geely Holding Group Co., the Chinese auto maker that owns Volvo Cars, is readying a bid for a majority stake in Malaysian car maker Proton Holdings Bhd., according to people familiar with the situation. France’s PSA Group, which makes Peugeot and Citroën cars, said Tuesday that it has submitted a bid.

China’s economic influence is growing in Malaysia, with a raft of deals in recent years. Geely executives recently visited Proton’s offices in Malaysia, said one of the people familiar with the bidding process. Geely’s public-relations manager, Ash Sutcliffe, declined to comment on Proton.

Proton owner DRB-Hicom Bhd. said earlier this month it expects to pick a foreign strategic partner for the unit in the first half of the year. The Malaysian automotive-to-defense conglomerate, controlled by Syed Mokhtar Al-Bukhary, didn’t name the interested parties, though local press linked both PSA and fellow French maker Renault SA to Proton.

“Assuming control of Proton would make good strategic sense for Geely as a play for the Southeast Asian market,” home to more than 630 million people, said Yale Zhang, managing director of Automotive Foresight. Cars built in any of the 10 members of the Association of Southeast Asian Nations can be sold throughout the bloc tariff-free.

While auto makers from Europe, Japan and the U.S. already have a strong presence in the region, Chinese makers have struggled overseas.

Proton was founded in the 1980s as a national industrial champion by a government eager to see Malaysia numbered among Asia’s fast-growing “tiger” economies, such as Japan, South Korea and Singapore. With Kuala Lumpur’s backing, Southeast Asia’s only auto maker came to dominate its domestic market, but it struggled to produce a profit, and dreams of marketing the Proton regionally as the “Asean car” fizzled.

Still, it remains a symbol of national pride, and a sale to Geely would underscore China’s growing economic clout in Malaysia, said Zhang Baohui of Hong Kong’s Lingnan University.

“China is certainly gaining influence over Malaysia,” said Mr. Zhang. “Its money is motivating Malaysia to redefine its China policy.”

On a visit to Beijing in November, Prime Minister Najib Razak signed $34 billion of deals, including an order for four Chinese-built navy ships and a $12.3 billion high-speed railway line that Beijing will fund on favorable terms. A year earlier China had agreed to a $2.3 billion rescue package for 1MDB, Malaysia’s scandal-hit government investment fund.

DRB-Hicom bought the Proton stake from Malaysia’s sovereign-wealth fund, Khazanah Nasional Bhd., for about $412 million in 2012.

Sales at Proton, which also owns British sports- and racing-car brand Lotus, continue to decline as debt grows. The Malaysian government extended a $282 million bailout earlier this year on the condition that it bring in a foreign partner.