DoorDash is looking to invest in the Berlin-based startup as part of a wider funding round.
The move marks DoorDash's first investment in Europe.
The report suggests that the deal could be finalised later this month, according to sources close to the deal.
Set up in 2020, Berlin-headquartered Gorillas has now expanded to more than 50 cities including New York, London, Amsterdam and promises to deliver groceries within an average of ten minutes.
Gorillas, which has hitherto raised more than $300m from investors including Tencent, directly employs riders and promotes its ability to deliver fresh grocers and household items at very short notice to customers at retail prices.
Goods are stocked in mini-warehouses in city centers and delivered by a fleet of riders, mostly on e-bikes.
The Berlin-based firm has recently faced protests over its treatment of its delivery drivers and warehouse workers, including complaints about poor working conditions.
DoorDash, based in San Fransisco, has a market capitalisation of $58bn and is now the largest US food ordering app by customer spending, according to industry figures, helped by it enjoying breakneck revenue growth.
In May this year, the Financial Times reported that DoorDash had been gearing up to launch in Germany, by posting job openings.