If successful, the deal to sell 6.4 million shares is expected to fetch VND66 billion (US$2.6 million).
The fund wants to sell out before Dec. 13, according to a disclosure to stock authorities.
Shares of Vinasun closed last week at VND12,250, down 72% from December 2013, when TAEL first bought three million shares.
Over the years TAEL increased its ownership to 18.3%, paying VND382 billion in total.
But since October last year it has been selling its stakes, and it has taken months to reduce the ownership to current levels as it struggled to find buyers.
Established in 2007, TAEL focuses on businesses in Southeast Asia, and has invested over $1.6 billion on companies in Malaysia, Indonesia, Thailand, Vietnam, Singapore, and the Philippines.
Vinasun, which mostly operates in HCMC, its neighboring localities and Da Nang City, reported a 52% decline year-on-year in profits in the first nine months of this year to VND60 billion.
With demand falling, the company has been selling old vehicles and carrying ads on its taxis to increase revenues.
It plans to buy 700 new hybrid vehicles this year, which it believes can reduce fuel expenses.