The office of Vice President Joe Biden and a Delaware newspaper on Sunday made it clear that Biden's son has not yet ruled out a run for Senate.

An earlier version of an article by Delaware News Journal reporter Harry Themal quoted Biden as saying that his son Beau does not want to run for Senate.

But Beau Biden has still not made clear his senatorial ambitions.

Here is the originally published back-and-forth:

Biden: "If you run into Beau, talk him into running; he respects you."

Me: "I don't think he wants to run, though."

Biden: "I don't think he does either. I know he doesn't want to. ... I'm so proud of the job he's done [as attorney general]."

Me: "Would you campaign for him [against Republican Mike Castle]?"

Biden: "Hell, yes. I told him I'd give him my sixth-born grandchild."

Later in the afternoon, ABC News' Rick Klein reported:

The vice president’s office contacted ABC News to say that Vice President Joe Biden was talking about convincing his interim replacement, Sen. Ted Kaufman (D-Del.) to run for a full term -- not, as the News Journal reported, his son, Beau.

A spokeswoman for the vice president provided this transcript of the conversation, and played me the audio of the vice president’s end of the conversation. The audio confirms the transcript below:

VP to Harry Themal:  Always a pleasure of seeing you buddy.  Talk Ted into running, if Beau doesn’t.   Talk him into running – he respects you.  I wish I had the power of appointing Senators.  I’d appoint him from Maryland if he wouldn’t do Delaware.

Harry Themal: "I don't think he wants to run, though."

VP:  No I don’t think he does either. I know he doesn’t.  I’m so proud of the job he’s done.  God.

Harry: Would you campaign for him?

VP:  Oh hell yeah, man.  I tell you what – I was joking if Beau didn’t run – I told him I’d give him my 6th-born grandchild. And you know, he said ‘I have enough of those.’ Alright, buddy, thanks.  (Call ends).

The News Journal followed by issuing a correction:

An earlier version of Harry Themal's column incorrectly said Vice President Biden said his son, Attorney General Beau Biden, did not want to run for the U.S. Senate. Vice President Biden was referring to Sen. Ted Kaufman, who currently holds the seat and has said he will not run for the seat in the November election.

This post was updated at 6:31 p.m.