Sen. Mark Warner sat down with CNBC's John Harwood to discuss a range of issues, including special counsel Robert Mueller's investigation into Russian meddling in the 2016 presidential campaign and possible collusion with Donald Trump's campaign. What follows is an edited, condensed excerpt of the conversation.

CNBC's John Harwood: Donald Trump Jr. at one point said, "a disproportionate share of our assets come from Russians." The president's had a long history of interaction with Deutsche Bank. And some people have wondered about the nature of those interactions with respect to Russia. How relevant are those facts to this picture?

Sen. Mark Warner: Those are not areas where the congressional inquiry has spent a lot of time, because we've not established enough of a nexus. I believe and hope that Bob Mueller is looking into this.

I think they're relevant for the following reasons. One, if we go back to what generated a lot of the smoke in the first place, the dossier. I don't believe that a lot of the dossier has been disproven. It would be so frightening if any parts of it are true. And so much of that dossier was built on the premise of these kind of financial ties.

Secondarily, we have heard a host of rumors. And rumors often-times coming from the press of the president's activities, because he wasn't able to be banked by many of the American banks, so banking through Deutsche Bank, and that there were Russian dollars that were in some mirror trading and helping to back some of those Deutsche Bank loans.

Just from a plain counterintelligence standpoint, that would set off a lot of alarm bells because of the fear of potentially being compromised or having undue influence. So for the president's own sake — assuming that there's no there there — I would hope that Mueller or others would expose this. Because if it's not true, we need to remove the cloud hanging over the president.

Harwood: Do you think that your inquiry and Mueller's, in a time sense, are moving on parallel tracks?

Warner: Well, I think we've actually interviewed more individuals than prosecutor Mueller. He's been pretty good about keeping things close to his chest. And he obviously has tools that we don't have.

But the fact that he has already elicited two guilty pleas, one from Mr. Papadopoulos, one from General Flynn, and he's gotten two indictments, of the president's campaign manager and deputy campaign manager, I believe he'll have many more stories to tell. I hope he moves with all due deliberate speed. We want to move with all due deliberate speed as well, but I think it's more important that we get this right.

Harwood: Do you think a year from now, both of you guys will be done?

Warner: Yes.

Harwood: You mentioned the president's criticism of some of those Republican appointed law enforcement officials. We're also seeing a drumbeat of criticism of the FBI, of Bob Mueller from conservative media. Do you think a predicate is being laid for Bob Mueller to be fired? And if so, how would your Republican colleagues react to that?

Warner: John, I hope and pray that's not the case. When Bob Mueller was appointed, he was greeted with universal acclaim. I think it's not fair. I think it's not right. I think it's frankly cheap shots when some of these Republican colleagues would question Mueller's integrity. And if you were to see a firing, I think you would see a constitutional crisis.

Harwood: Is this whole thing going to end up in a constitutional crisis one way or the other?

Warner: I think that is going to be up to what this president does or doesn't do. I mean, if this president allows this investigation to come to its conclusion and either bring charges or not, then I think the system will have worked as our founders intended. If they pull on one of these threads as a reason to fire Mueller, I think it will be a political disaster for the president, and I believe it will be a constitutional crisis.

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