Earlier this week, Hansen branded Gatland's complaints about All Blacks players diving at the legs of Conor Murray in the first test as "desperate", which gave rise to a slew of articles about how the two New Zealanders did not get on.
Hansen, whose side can wrap up the three-test series with victory at Wellington Regional Stadium on Saturday, played down suggestions that he was in a war of words with Gatland.
"I read somewhere that I, 'lashed out at Warren Gatland,'" Hansen said on Thursday.
"I haven't lashed out at Warren Gatland, at all. I've got a lot of respect for him and I'm looking forward to having a beer with him and a chuckle about life.
"We've got a lot of common interests. He likes racing horses and so do I. He coaches Wales and I've been through that experience myself.
"It's the media that ramp it up because it sells you guys' newspapers. Who am I to say stop it? But I do look at it and say 'well, that's actually not how it went.'"
Hansen also hit out at the New Zealand Herald's decision to run a cartoon depicting Gatland as a clown, echoing a similar effort targeting Australia coach Michael Cheika last year.
"I think it's really disappointing. It's one thing to have a bit of banter and you guys beef that up to make it bigger than it really is," Hansen added.
"To come out and do that is ridiculing somebody. He doesn't deserve it and, at the end of the day, we're all coaches trying to do what we think's right."
Gatland also spoke about the supposed feud on Thursday.
"I have tried to be complimentary of the All Blacks," he said. "They're the best team in the world.
"It has been a great experience. The hospitality has been fantastic. The treatment we have had from the fans has been absolutely brilliant.
"I don't think there is any hostility from this side, hopefully we can have a good game and beer afterwards."
The series concludes on July 8 at Eden Park in Auckland, where the All Blacks won the first test 30-15
(Writing by Nick Mulvenney in Sydney; Editing by Peter Rutherford)
