OCBC and related companies own around 36 percent of United Engineers, valuing their combined stake at about $514 million at the stock's current price.
News of the possible deal first broke last week.
A potential sale would also trigger a takeover offer for United Engineers, which has a market value of about $1.4 billion. Under Singapore rules, a company that acquires a stake of 30 percent in a listed firm must make a mandatory offer for the remaining shares.
OCBC and Great Eastern Holdings said on Wednesday the talks with TCC Top Enterprise Ltd, controlled by Charoen and his wife, are at a preliminary stage and the exclusivity agreement will last for six weeks.
OCBC's announcement comes a day after United Engineers said its subsidiary WBL Corporation was selling its luxury car business to StarChase Motorsports (Singapore) Pte Ltd for S$455 million($365 million).
Shares of United Engineers have risen by more than a fifth since last week. The stock rose as much as 2.5 percent in morning trade, before paring gains to trade up 1.1 percent, while the broader Singapore market was up 0.4 percent.