According to Sky News, a float is expected to take place in London next year, and is set to value the delivery company at more than £2bn.
Deliveroo declined to comment on Goldman's appointment, and sources close to the company insisted this weekend that there was no definitive timetable for a public listing.
Further banks are expected to be appointed in the coming months.
Sources said that Deliveroo now had 44,000 restaurants on its platform in the UK, as well as 16 on-demand convenience and grocery partnerships with the likes of Waitrose, Morrison's, Aldi and the Co-Op.
In total, those partnerships cover 1,000 new stores on the Deliveroo app.
The Amazon-backed company is now preparing to launch a series of new features aimed at strengthening Deliveroo’s appeal to customers, restaurants and riders.
These will include post-order tipping - allowing customers to reward riders after their delivery has arrived - in the UK and a number of other markets.
Deliveroo also plans to offer a group-ordering function in its app which enables customers to share a single ‘basket’ among several users without the need to pass a mobile phone between different people.
Sources told Sky this was likely to benefit restaurants through larger orders from multiple people in the same household or office.
The company is also expected to announce the launch of a service called Brought to you by Deliveroo, which will allow customers to order food from restaurant websites, but with the tech company fulfilling the delivery.
It is said to be the first time that a delivery platform will have offered such a service in Europe and Asia, and is being tested with chains including Nando’s.
During the summer, Deliveroo ended a nine-month search for a permanent finance chief by appointing Adam Miller, a former executive at the travel group Expedia, to the role - a move which stoked speculation about its IPO preparations.