Referee Don Robertson sent the Austrian off just two minutes after he came on as a substitute near the end of Hearts’ 2-1 win against Dundee.
The result moved the Edinburgh club 15 points clear at the top of the Championship, but Haring is facing a suspension unless an appeal is submitted.
He was issued a straight red card for a high tackle on Dundee’s Declan McDaid and left the field adamant he didn’t touch his opponent.
“I thought it was a yellow right away at the time,” said Hearts manager Robbie Neilson “The ref has a different angle and he’s got the red out. I haven’t seen it but I will have a look at it and make a decision.
“It’s tough for Peter in that he’s just come back into the team and he’s got a red card card. He’s working away trying to get himself fit and bet back in the team. He gets a chance and then gets sent off and, potentially, suspended.
“We will make a decision on whether we appeal it or not.”
Hearts moved 2-0 ahead in the game through Andy Halliday and Armand Gnanduillet before Jason Cummings’ penalty led to a nervous ending.
“At 2-0 we were quite comfortable but then you give away the penalty and start getting a bit edgy, which is understandable when you’re going for a title,” said Neilson.
“We created a lot of chances and should have scored more, definitely, but it’s another three points and we’re in a good position in the league.
“It's good to be 15 clear but Raith Rovers have three games in hand so we still have quite a bit of work to do.”
Asked about a verbal altercation with the Dundee manager James McPake at full-time, Neilson replied: “It’s just two managers desperate to win and two teams going for the league.
“Here, where you’re a yard and a half away from each other and everyone wants every decision, there’s always a wee bit of edge. To be honest I quite like that but once the final whistle goes, that’s it done.”