Tan, the Malaysian multi-millionaire businessman, took control of Cardiff in 2010 by buying 36.1% of the club.
The process to float shares is said to be at an early stage, with the initial plan to list Cardiff on the Kuala Lumpur Stock Exchange.
Tan has promised to spend £25m on players this summer as Cardiff prepare for the Premier League.
Tan, who was unavailable for comment, had been quoted in the Malaysia press as saying he would consider offers for the Welsh club, but later said he would "like to be here for the long haul".
Should Cardiff make an initial public offering (IPO) on the stock exchange, they would become the second Premier League side to float shares in the past year.
Tan pushed through a controversial rebranding at Cardiff in June, changing the club's home colour from blue to red and introducing a new badge.
He said Cardiff's success this season justified his decisions, but hasruled out a name change and any further rebranding.
Tan is Malaysia's 10th richest person with a net worth of $1.3bn, according to business magazine Forbes.