Based in London, Deliveroo is valued at more than $2 billion.
No talks about acquisition price have come out in the public.
The value of the proposed deal is not known, according to Bloomberg, which first reported on the talks, citing people familiar with the matter - but they would likely have to be for more than $2 billion, the United Kingdom company's latest valuation after raising $98 million.
However, its too soon to say if the talks will go through, with sources saying Deliveroo and its investors have been reluctant to relinquish independence.
American food delivery and ride share company Uber is reportedly looking at purchasing UK-based delivery firm Deliveroo. It is omnipresent in European capitals, and globally it is available in over 200 cities on four continents.
More than 100 Uber Eats couriers blocked roads in London on Thursday to protest what they said is a significant cut in pay by the company.
Edward Park, investment director at Brooks Macdonald, meanwhile told Reuters that "Uber's deep pockets combined with an acquisition puts a lot of competitive pressure on the other food delivery companies over the medium term". After selling its ride-hailing businesses in Southeast Asia, China and Russia, Uber is eager to buy competitors, rather than sell its remaining local businesses.
Deliveroo is one of Europe's biggest startups and past year raised about $480m from investors including Fidelity Investments and T. Rowe Price Group Inc.
A merger would lead to a "war for market share" that would be "very damaging" to Just Eat's profits, analysts at Canaccord Genuity said.
Deliveroo was in financing talks previous year with SoftBank, one of Uber's major investors; the negotiations ended after SoftBank concentrated on backing Uber. The negotiations abruptly ended after SoftBank concentrated on backing Uber.