The Wirtschaftswoche business magazine first reported the news, saying Singapore's Grab could pay a little more than €1 billion ($1.07 billion) for the unit.
The Berlin-based company plans to sell its activities under the foodpanda brand in Singapore, Cambodia, Laos, Malaysia, Myanmar, the Philippines and Thailand, it said in a statement.
Investors in the online takeaway food company welcomed the report, lifting its shares as much as 13.5%.
Grab did not immediately reply to an emailed request for comment.
Delivery Hero has been focusing on reaching profitability while maintaining growth as investor confidence in the company started to wane after a pandemic-driven boost.
The group has said that it reached an adjusted profit before interest, tax, depreciation and amortisation (EBITDA) in the first six months of the year, although it did not quantify it, after a loss of €323 million in the same period a year earlier.
Last month, chief executive Niklas Oestberg said that Asia was the segment where the company saw most opportunity to invest.
Singapore internet firm Grab posted $567 million (€532.2 million) in revenue in the quarter that ended 30 June and expects to break even on an adjusted core earnings basis in the current quarter.
Grab makes most of its sales from its food delivery business and has recently seen strong growth in its ride-share business.
Earlier this year, Delivery Hero said it would offer investors significantly higher interest payments than it has done historically to raise €1 billion through a new seven-year convertible bond.