"We remain squarely focused on delivering shareholder value. As we have consistently said, consolidation could make sense in our industry, and, like any responsible company, we are always looking at value-enhancing opportunities," GrubHub's statement said.
"That said, we remain confident in our current strategy and our recent initiatives to support restaurants in this challenging environment."
Grubhub shares were halted for trading for a second time on the New York Stock Exchange Tuesday after jumping more that 35% following multiple reports that Uber was interested in acquiring the company.
Twitter user @deltaone tweeted that Uber approached Grubhub with a takeover offer, leading to a jump in the stock.
The Wall Street Journal is also reporting the approach, citing sources. The Journal reported that GrubHub is seek 2.15 Uber shares for each share of GrubHub.
Grubhub declined to comment on the story while Uber was not immediately available for comment.
The NYSE's circuit breaker kicked in, pausing trading of the stock for 10 minutes. At last check the stock was 23% higher at $57.63.
The field is sharply competitive, with rivals also including DoorDash and Postmates.
The services have been a prominent focus for investors and analysts.
During the pandemic their services have enabled people to order in while sheltering at home.
But they have also come under fire for their pricing practices, with some restaurants saying that the delivery fees are high enough to render customer orders unprofitable for them.
Both Grubhub and ride-hailing company Uber reported their earnings results last week.
“While our Rides business has been hit hard by the ongoing pandemic, we have taken quick action to preserve the strength of our balance sheet, focus additional resources on Uber Eats, and prepare us for any recovery scenario,” said Uber Chief Executive Dara Khosrowshahi.
"The restaurant industry is facing enormous challenges in light of the difficult, but necessary, steps taken to keep us safe as we fight covid-19," Founder and Chief Executive Matt Maloney said in a statement.
"Grubhub is using nearly all of our profits in the second quarter to generate as many additional orders for our restaurant partners as possible. We hope that the darkest days are behind our restaurant partners and they can start focusing on the recovery."
Grubhub has a market cap of more than $5.3 billion as of Tuesday. Uber has a market cap of $57 billion.