Jenkins, 28, said: "2005 was a great experience for me but it's unfinished business because we didn't win the series. Paul O'Connell was the only other forward to start that first Test against the All Blacks and he will say the same.
"Paul is a great captain and a great competitor - you can see that from the way he plays for Munster and Ireland.
"We became very good friends when we toured together in New Zealand and I've got a lot of respect for him both on and off the field. It's great to be in the squad but when you go out on the tour, the main goal is to be in the Test team."
Double Grand Slam winner Jenkins is joined by fellow Wales prop Adam Jones and hooker Matthew Rees in Ian McGeechan's 37-man squad. And the Cardiff Blues star believes it will be a great feat to complete a front-row hat-trick.
Jenkins said: "It's great to see Adam and Matthew also included in the squad. I was the only Welsh front five player in the squad last time so I hope we can all make an impact this time around."