Police are making enquires into an incident involving Craig Brown, 70, and his former employer at Motherwell, Fir Park chairman John Boyle.
Brown, now Aberdeen manager, appeared to react angrily to a word in his ear by Boyle as the pair shook hands at the end of Motherwell's 2-1 win.
"We are not looking at any form of criminal inquiry," said superintendent Brian Connel, the match commander.
"But given what we have seen at other grounds it's right we make enquiries."
The incident was remarkably similar to the now infamous one involving Celtic manager Neil Lennon and Rangers assistant boss Ally McCoist.
Just like that altercation at Celtic Park last month, there was a rush to separate the two men but the police were not involved in this.
Superintendent Connel added: "I think there was an exchange of words and very minor pushing thereafter so we just wanted to make sure there was no criminal element to that. We have not identified any criminal element.
"Nonetheless with the assistance of both clubs we will make sure we get to the bottom of it."
Soon after the incident Brown told BBC Scotland: "I would love to be able to speak about it but it's in the hands of the police now.
"I've spoken with the police officer in charge of the match and he said that it's best not to make any comment about it.
"They were very fair. They saw the incident. I am very pleased they saw it. I have left it in their very capable hands."
And while speaking favourably of the players at Motherwell, Brown took a swipe at the Fir Park outfit.
"I could have said many things which might have embarrassed the football club, but I didn't, so I will continue to keep that dignified silence as long as I need to," he said.
"But I think it would be revealing if the fans heard some of the things that I could say."
The Scottish Premier League match was Brown's first return as Dons boss since leaving the Steelemen for Pittodrie.
However, his former team were deserving 2-1 winners, thanks to goals from Chris Humphrey and Shaun Hutchinson, though Aberdeen did pull one back in injury-time through Nikola Vujadinovic.
"The better team won the game," Brown said. "I wish them all the best in the top six, which I am sure they will consolidate.
"We would have had a chance if we had a full-strength team but we had seven players missing."