"We played some shows with him (Sean Lennon) in America... He's a trippy kind of dude," Parker says.
"Trippy" is also a good description of the psychedelic melodies the ARIA award-winning band are known for producing. Their 2012 album Lonerism falls into the "hypno-groove" genre. Think the Beatles during their Ravi Shankar period.
Comparisons aside, Tame Impala's hypno-grooves create a natural high that are all their own. Parker says that's "a small part of the idea" behind creating the music.
"I definitely think that one of the purposes of psychedelic music is to have a kind of an effect on you that's like you're on drugs only you can't have any drugs, or you don't like drugs," Parker says.
"Sometimes I get stoned when I'm making music, sometimes I get drunk. Sometimes I get both. Sometimes I'm completely sober. In the end it doesn't really matter. The only thing that matters is that you're getting something out of it, or that it's moving you."
With three 2013 ARIA awards (Album of the Year, Best Group and Best Rock album) and a 2014 Grammy Award nomination (Best Alternative Music Album) the group are clearly moving the right people.
But Parker doesn't think 2014 will be Tame Impala's year at the Grammys, as they battle bands such as Vampire Weekend and The National for the award.
"We're up against bands that people have actually heard of. People aren't going to be confused if Vampire Weekend win, but if they read out 'Tame Impala' everyone's going to go, 'Who the f*** is Tame Impala?"'
While the groups start to make ripples in international waters, the waves of success at home have propelled them towards one of Australia's biggest festivals, Big Day Out. But Parker is modest about that, too, saying he's excited at the prospect of meeting his own music idols there.
"I was actually a massive Deftones fan (set to play Big Day Out 2014) when I was in high school, so that's going to be a trip down memory lane," he says. "And hopefully I'll get to meet them, that would be even better."
So what's next for the successful producer/songwriter/performer?
Parker wants to go right back to the beginning.
"I'm always recording," he says. "The thing at the moment is I'm trying to stop myself from recording. When I start back up again, I want to have forgotten everything I know about music."
He wants to regain some of the naivety he had for making music before his success.
"I just understand things a bit too well now. So I'm trying to wait until I've just forgotten... In fact, I've already forgotten how to write a song," he says.
"I realised quite seriously that I don't know how to write a song and it makes me wonder how the hell I put together a whole album."
But Parker will inevitably find his way back on to the mystery tour again.
"For me, music is the thing that gets me there," he says.
"It just takes me miles higher than anything else."
* Tame Impala will play Big Day Out in Auckland, January 17.
- AAP