The war between the pair blew up at the weekend when Hamilton felt that Rosberg had driven off the road deliberately in qualifying in a bid to secure pole position by disrupting his team-mate's lap with yellow flags.
A stewards' investigation into Rosberg's actions ruled that he had done nothing wrong, so he kept the pole position that helped him to an important win.
Fresh off the back of a row between the two drivers at the Spanish GP, when Rosberg was upset that Hamilton went against team protocol to turn his engine settings up in the closing stages of the races, relations completely broke down between the pair.
AUTOSPORT understands that the two men are no longer on speaking terms, and it was their lack of communication during post-race ceremonies that has particularly upset Lauda.
When asked by AUTOSPORT about concerns of distrust between his drivers, Lauda said: "Lewis not happy finishing second is normal, but in the end he has to accept another guy was quicker. This is very simple in racing.
"What I did not like, and I have to say, and I will tell him this on Monday, is that when you are up there [on the podium] and you don't say hello to your team-mate, which Nico has always done, that is not good.
"It's not because I am well educated, but it's for the brand Mercedes. This is something I start to worry about now, but it's easy to fix."
Hamilton conceded that the Monaco podium was the first time there had been no communication between himself and Rosberg after the race.
"We never really speak on the podium," he said. "The last four podiums I will just say well done to him, and after we would say this is unbelievable what the team has achieved.
"This weekend we didn't. But we will I'm sure in the future."
LAUDA VOWS TO SORT IT
Lauda plans to talk to both drivers in the coming days to get their perspectives on the situation at Mercedes, and he is hopeful that things will be better in Canada.
"I spoke to the drivers before the race and it is not finished," he said.
"I understand all the comments and I have to wait two or three days, but before it goes to Canada it will be solved.
"I will speak to them like I always do. They always call me when they have problems, so I think it will sort itself out.
"It is normal. I had the same with [Alain] Prost. I hated the guy, but at least I said hello in the morning.
"There are certain limits and these certain limits I can reintroduce because I speak their language, the drivers' language, and they do understand me, they like me and there is no issue."
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