The transaction is set to be matching and put through from Dec. 14 to Jan. 12, the jewelry company stated.
After the transaction, Dung is set to own 6.3 million shares, or a 2.8 percent stake.
With PNJ priced at VND97,700 Monday ($4.25), the value of the deal is estimated at around VND488 billion.
Dung said the reason for the transaction is personal.
Dung’s brother Cao Ngoc Duy has also registered to buy 4.5 million PNJ shares through matching and put through orders.
This will increase his ownership in the company by 1.98 percentage points to 2.9 percent.
PNJ is recovering after plunging from the peak of VND110,000 since mid-November.
BIDV Securities at the end of last month forecast PNJ could reach VND126,100 within a year.
The company saw post-tax profit falling 15 percent year-on-year to VND697 billion ($30.3 million) in the first 10 months due to Covid-19 impacts.