Speaking to MSNBC’s Rachel Maddow Thursday, Vice President Biden said President Obama would choose "a consensus candidate" to fill the Supreme Court vacancy left by the late Justice Antonin Scalia.

Biden, who chaired the Senate Judiciary Committee from 1987 to 1995 and has helped advise the president on his previous picks for the nation's highest court, said he has "faith" Obama will select a highly qualified candidate with the right background and temperament as a nominee.

"I think we ought to be able to find a consensus candidate that meets that criteria," Biden said during a taping of “The Rachel Maddow Show” in St. Paul, Minn.  "Because the Senate does have a right to have a say in who -- and what the philosophy of the nominee is.  But they only get to dispose.  The president proposes."

Biden recalled how he consulted with Ronald Reagan when two of his Supreme Court nominees -- first Robert Bork, then Douglas Ginsburg -- failed to win sufficient Senate backing.

"And Ronald Reagan called me down to the Oval Office. And Howard Baker was then his chief of staff.  So the three of us sat in the Oval. And he sat down. He was gregarious.  And he said, 'OK, Joe, who do you want?'" Biden recalled. "And I said, 'Mr. President,' I said, 'Yours is to propose, mine to dispose.'  I said, 'You tell me who you have in mind, I'll give you an honest answer what their chances are in my view.'"

"So he then read off to me the potential nominees he had in mind. And with Howard there, I told him, 'Mr. President, I think that that person will have -- suffer the same fate as Bork; this person I think would probably get nominated; that person would...'" he added. "And you know, that's part of the advise and consent process."

"So should President Obama do that with Senator Grassley?" Maddow asked, referring to the current Judiciary Committee Chairman, Charles E. Grassley (R-Iowa).

"Yes," the vice president replied.

"Do you think he will?" Maddow pressed.

"Yes, I'm confident he'll -- he'll reach out to the Senate and go through the process of advise and consent," he replied.

Biden also dismissed the idea that Obama would choose him as the next Supreme Court nominee, saying, "I have no desire to sit on the Supreme Court, none."