In the interview, Reid also defended Connecticut Sen. Joe Lieberman, after the former Democratic vice presidential nominee accepted a speaking slot at next month's Republican convention in Minnesota.
"He has a close personal relationship with John McCain. I don't fully understand why he does," Reid told the paper.
"I told him last night, 'You know, Joe, I can't stand John McCain.' He said, 'I know you feel that way,' "
Reid said Lieberman called him Tuesday from the Republic of Georgia to tell him he would be speaking at the Republican convention.
McCain and Reid have long had a testy relationship, with Reid repeatedly questioning if McCain has the "temperament" to be commander in chief.
Reid also called fellow Democratic Sen. Joe Biden of Delaware "the odds on favorite" to be Sen. Barack Obama's running mate.
In an interview with Politico earlier this week, McCain said "the first thing" he would do as president would be reach out to the Speaker of the House and the Senate majority leader.
"I [would] go to see the speaker of the House and the majority leader of the Senate — I assume that that would be Sen. Reid, I hope not, but I think that’s probably the reality of this election — and I would say, 'Let’s have an agenda, let’s work together," McCain said when asked how his approach to governance and politics would differ from Bush.