The company is believed to want to make a quick appointment and agencies are expected to answer initial briefs this week.
Deliveroo has been advertising on the London Underground with posters showing off the different types of cuisine it delivers with the tagline: "From the chef to your door."
The business teams up with restaurants to deliver their food to local homes and offices between noon and 11pm daily. The service is available in 11 countries outside the UK, including Australia, Germany and the United Arab Emirates.
Deliveroo did not respond to Campaign’s requests for comment.