The Chicago company has enlisted financial advisers to consider such a sale or an acquisition, people familiar with the matter told the paper.
They also said the company is planning what to do in case an activist investor preys upon it.
Grubhub, which went public in 2014, saw its shares soar 156% from January 2016 to August 2018.
But since then the stock has shed 61% amid heated competition from other delivery companies. Discounts are the norm in this industry, compressing profit margins, and many of the players aren't likely to survive.
Grubhub is suffering from decelerating customer growth. In October it lowered its profit and revenue forecasts.
Morningstar analyst Ali Mogharabi issued a scathing report about Grubhub after its October earnings release.
“Grubhub has finally realized that it lacks differentiation from most of the other players in the online meal takeout and delivery market, which supports our view that this firm has always lacked the network effect moat source,” he wrote.
He was also unimpressed with Grubhub’s response to the problem: paying up to obtain more customers.
“We disagree with this strategy and believe Grubhub should focus more on profitability rather than growth, which comes at the expense of commoditizing all its services, not just delivery,” Mogharabi said.
Grubhub’s shares at last check stood at $55.58, up 14%.