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The build-up to the second Test has been dominated by the two coaches exchanging views in the media.
On Sunday Gatland accused the All Blacks of using dangerous tactics, with Hansen calling his fellow Kiwi "desperate" in response.
"I've got a lot of respect for him," Hansen said.
"You guys [the media] are having a field day between Gats and I so I'm not feeding it. I haven't lashed out at Warren Gatland at all.
"I'm looking forward to having a beer with him and a chuckle. We have a lot of common interests. He likes racing horses, so do I. He coaches Wales, I have been through that experience myself."
Gatland told the media on Sunday the All Blacks had targeted scrum-half Conor Murray during their 30-15 first Test defeat in Auckland and could have caused a career-ending injury.
But New Zealand flanker Jerome Kaino insisted there was no malice or intent behind his challenge on Murray.
Hansen also turned on his national newspaper The New Zealand Herald, who mocked up a picture of Gatland as a clown on their front page.
"It's one thing to have a bit of banter and [the media] to beef that up to make it bigger than it really is," Hansen added.
"[But] you are ridiculing someone who doesn't deserve it. To ridicule someone is not right, so it's a bit disappointing really."
Meanwhile, Gatland says there has been "no hostility" from the Lions towards Hansen and the All Blacks.
"I think I've been pretty mild and have tried to be complimentary of the All Blacks, obviously they are the best team in the world," Gatland added.
"It's been a great experience for us as a team. Hopefully we can have a good game of rugby and maybe enjoy a beer together afterwards."
New Zealand coach Steve Hansen has played down the war of words with Lions counterpart Warren Gatland, and insists there is no animosity between the pair.