He suffered a collapsed lung during the incident and had what doctors believe was a mild heart attack.
Whittington still has about 30 pieces of shot inside his body and speaks with what he describes as "a warble" caused by one that pierced his larynx. Another is near his heart, too deep to remove safely.
Cheney has not apologized in public for the shooting, and when asked by the Post if Cheney had done so in private, Whittington paused, then said sharply: "I'm not going to go into that."
The Post said Whittington was "too gracious" to say Cheney had not said sorry, but also did not dispute he had not received an apology.
Despite this, he told the paper that he regarded Cheney as "a very capable and honorable man."
"He's said some very kind things to me," Whittington said.
After the shooting, Whittington issued a statement saying he and his family were "deeply sorry" for "all that Vice President Cheney and his family have had to go through."
But he told the Post he had not meant his apology to be taken as an admission that he was responsible for what happened.
"It really wasn't that. I didn't intend it that way. It was more of a sense of disappointment that it happened at all," Whittington said, according to the paper. "I'm sure it must have been difficult for Mr. Cheney and his family. I still feel the same way."
In the interview, Whittington said he was not bothered that the White House had initially blamed him for the incident, with a Bush administration spokesman at the time saying Whittington had failed to follow the correct protocol during a quail hunting trip in Texas in February 2006.
"Naturally, people want to make it appear that it's someone's fault," he told the Post. "I didn't care. Plain and simple, it was an accident. It could happen to anyone."
Whittington said he had gone hunting since, but added that "some of my enthusiasm is gone."
"I was lucky. I just feel like every day is a gift. Sometimes I wonder why I got these extra years," he told the Post.