The seven-time Tour de France winner and the actress were spotted in Austin on both Friday and Saturday nights. First, the pair dined at Eddie V's, a high-end restaurant frequented by Armstrong, according to a restaurant insider.
"They came in [Friday] and had dinner together, it's true," the insider tells PEOPLE.
The next night, Hudson, 29, and Armstrong, 36, ate at the casual Hula Hut with the athlete's three children and a group of friends. "They came in with the kids and a large group of people," says another restaurant source. "They ordered dinner – tacos, burgers and fries and that sort of stuff."
Asked if the pair looked romantic, the source merely said, "They looked like they were having fun."
Hudson and Armstrong were also in the same place on Thursday: Both were spotted in New York at the Wildwood Barbeque restaurant at the afterparty following Kid Rock's Madison Square Garden concert.
Hudson, who has been filming Bride Wars, recently called it quits with her on-again, off-again boyfriend Owen Wilson. Armstrong was most recently linked with Ashley Olsen.
Armstrong's rep had no comment. Hudson's rep does not comment on clients' personal lives.