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.