Mr Kenny warned his cabinet ministers this week to watch what they say about the economy after Mr Varadkar suggested Ireland may need a second bailout.
The Taoiseach made the comments during a political discussion with ministers at Tuesday's cabinet meeting.
But the Irish Independent understands Mr Kenny had a separate one-to-one conversation with Mr Varadkar about his comments.
"He spoke to Varadkar afterwards and was more direct," a coalition source said.
Mr Kenny yesterday laughed off suggestions of having a specific talk to Mr Varadkar -- but he didn't deny such a conversation had taken place.
"I speak to my ministers on a regular basis, both individually and collectively, as any good Taoiseach should," he said.
Mr Varadkar yesterday insisted he has not been "confined to barracks" for suggesting that Ireland may need a second bail out.
He denied being slapped down by Mr Kenny for his comments to 'The Sunday Times' where he said it was unlikely that the State could return to the bond markets next year.
The minister made his first public comments about the remark before addressing a conference organised by Engineers Ireland in Dublin yesterday.
Mr Varadkar claimed his remarks were "hyped up" and that he did not wish to comment further.
Asked if he was slapped down, he said: "I wouldn't say that. I was in the Dail yesterday (Wednesday) and I'm travelling to London this evening to address Enterprise Ireland so I'm certainly not being confined to barracks or anything like that.
"I would say the story hyped up my comments. I don't want to say anything more about them because it is such a sensitive issue. The Government's intention is clear. We intend to go back out to the markets in a small way in 2012 and get back fully in 2013."
Mr Varadkar's comments follow similar sentiments from Finance Minister Michael Noonan on Monday when he said the State would return to the markets by the end of next year.
Asked if there was any lessons for him out of the interview, Mr Varadkar added: "There probably is, but we will share them another day."