Stoke boss Mark Hughes confirmed afterwards that Shawcross was booked in the dressing room during the interval.
“Ryan was booked in the dressing room. I’ve no idea why," he said.
“I’ve never known anyone get booked in the dressing room before.”
The pair clashed over a corner during the Red Devils' dramatic 3-2 win at Old Trafford and continued their disagreement at the half-time whistle.
The Sun report that the pair came together once more at the end of the game when the Manchester United striker appeared to mutter something at Shawcross during a television interview.
The paper quote an eye-witness as saying: “It wasn’t clear what RVP said but Shawcross wasn’t happy at all. He asked Robin to repeat what he said a couple of times but he just kept walking.
“There’s been bad blood between RVP’s old club Arsenal and Stoke for a few years now, so perhaps it stems from that.”
Van Persie was part of the Arsenal squad when Shawcross broke Aaron Ramsey's leg in a game back in 2010.