I have spent many hours with him in private conversation.

He seemed to have his own idea of a private conversation.

As a matter of fact, we were having a private conversation in here.

I asked him when we seemed to have a moment clear for private conversation.

This was a place where a private conversation could be held.

"There should have been a private conversation and a meeting."

"How did you come to be present at this private conversation?"

It was a private conversation and I don't know what happened.

"With senior staff, when you really need to get away from the office and have a private conversation."

Remember, too, that we must not be seen in private conversation after this.