The two firms were not in agreement on a deal that would unite two of the three largest US players in the food delivery segment, according to the source who declined to be identified.
The $6 billion share offer was first reported by The Wall Street Journal.
Grubhub shares, which rose sharply on the reports of a tie-up earlier this week, slipped 3.7 percent on Wednesday.
Neither company commented on the potential tie-up but Grubhub said in a statement it is "squarely focused on delivering shareholder value" and added that "like any responsible company, we are always looking at value-enhancing opportunities."
Uber has been seeing strong growth in its food delivery operation Uber Eats, partly offsetting the sharp decline in ride-hailing during the global pandemic.
According to the research firm Second Measure, Uber Eats accounted for 20 percent of US meal delivery sales in March and Grubhub had 28 percent. A combined operation would overtake number one player DoorDash, which had 42 percent.
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