The Glad You Came hitmakers re-located to Los Angeles earlier this year (13) to record their new album, and allowed cameras for America's E! network to record their time in the U.S. for fly-on-the-wall series The Wanted Life.
The show debuted earlier this month (May13) and the group is now in talks for another season - but Parker admits not all the bandmembers are in favour of a follow-up.
He tells Britain's Daily Mirror, "A few of the boys didn't want to do another series, but I think it's good for us, it's great exposure.
"They're talking about it at the moment. I think it's going to happen which is good. You don't want to do a season and then be forgotten about."