And now, according to People, the actress and the baseball player are getting serious.
"It's somewhat serious," a source told the mag. "He introduced her to a bunch of his friends."
Kate reportedly followed A-Rod on the road last month while he played the Texas Rangers in a three-game series.
According to the mag, Kate and son Ryder, 5, stayed in the same hotel as the Yankees third baseman.
Kate and A-Rod "worked out together in the fitness center," an eyewitness claimed.
During one of the three games against Texas, Kate reportedly sent Ryder to the ballpark to watch the game with his nanny, while she "stayed behind and watched the game from the hotel," added the eyewitness.
"She remarked several times about what a big baseball fan she is!" the eyewitness said.
But will the reported new couple be able to hit their romance out of the park?
According to another People source, it's too soon to call this one.
"You never know with Kate," the source said.