Insiders suggest that the deal for the Asian businesses will be worth a total of $225 million, the Wall Street Journal reports.
Meanwhile, three sources also indicated to news agency Bloomberg that Nomura is also set to snap up Lehman's European investment banking and equities units.
Its main rival remains London-listed Barclays bank - although the firm is only thought to have bid for the equities business.
Dan Schwarzmann at accountants PricewaterhouseCoopers, which is administrating the bankrupt bank, suggested today that Nomura is the frontrunner in the deal.
"We are now focusing on one party as they are interested in acquiring a wider team, which should result in a better deal for staff and creditors," he commented, declining to name the firm.
"Given the complexity of Lehman, these negotiations are difficult, but I'm hoping to give certainty to all involved in the short term."
Neither Nomura or Lehman's Hong Kong office has commented on the supposed deal.