The 29-year-old founder of Singapore's BandLab Technologies already owns 49 per cent of Rolling Stone. Now, Mr Kuok Meng Ru, a member of one of Asia's richest families, said he is in talks to take over the magazine.
Mr Jann Wenner put up his controlling stake for sale two months ago, relinquishing his hold on the publication he co-founded in San Francisco in 1967.
"We really believe in building on the legacy and making sure we continue the vision that Jann started," Mr Kuok said.
"That's why we got involved in the first place. We have a great relationship with the Wenners."
Like other consumer magazines, Rolling Stone has struggled with declining newsstand sales and an online advertising market dominated by Facebook and Google.
American media reported that three other bidders are also interested in buying Mr Wenner's stake.
Mr Kuok acquired his 49 per cent holding last year after striking a deal with Mr Gus Wenner, heir apparent to a business built around his father's magazine.
Mr Kuok then established Rolling Stone International to expand the brand, including signing a licence agreement with Japan's CCC Group to publish Rolling Stone in Japan.
The magazine made its mark in the 1970s and 1980s with cutting-edge music and political coverage.
Mr Kuok, the third child of Mr Kuok Khoon Hong, the co-founder of Wilmar International, the world's biggest palm-oil company, launched BandLab last year as a social network for musicians and fans after graduating from Cambridge University.
Since then, the company has doubled its payroll to 80 and its BandLab app has two million registered users making about 10 songs a minute.
BandLab has made a series of acquisitions, including Chew.tv, a London-based video-streaming service for DJs, and Mono Creators, a San Francisco-based company that makes high-end instrument cases.
It has also developed products in Singapore to help people make and play music more easily using their mobile phones.
In 2012, Mr Kuok Meng Ru acquired Swee Lee, a 71-year-old distributor of guitars in Singapore. He plans to launch a flagship store here on Monday that combines instruments, fashion, a music academy and a coffee shop.