At $54 per share, Grubhub's stock is closing in on the price it traded at before its disappointing third-quarter earnings report in October.
In addition to a possible sale, Grubhub is also weighing the possibility of an acquisition and has discussed strategies for fending off activists, according to the Journal. The review is still at an early stage, and it's possible that it won't lead to any strategic moves.
A Grubhub spokesperson told CNBC that the company doesn't "comment on market rumors or speculation."
Uber shares also spiked on the news, as investors bet consolidation in the crowded food-delivery industry would help the company. They ended the day up 3.4%.
Grubhub has seen its market value dwindle as it continues to buckle under pressure from competitors, including UberEats, DoorDash and Postmates. The company's market cap now stands at $5 billion, up from earlier Wednesday, when it stood at roughly $4.4 billion. However, Grubhub's market cap is still far below where it was one year ago, when it was valued at about $7.3 billion.
In its third-quarter earnings report, Grubhub also gave weaker-than-expected guidance for the fourth quarter. The company cited weaker order frequency as one of the catalysts. Grubhub has ramped up its marketing spend to better compete with its rivals, which have flooded the market with rewards and incentives, causing consumers to shift from one service to another.
— CNBC's Jim Forkin contributed to this report.