The 26-year old has one year left on his current deal with North Queensland and new Titans coach Justin Holbrook reportedly has him in his sights.
Asiata met with Holbrook in November when he was Brisbane for a wedding.
“Right now my focus is (with the Cowboys), I can’t really do anything outside of football. My job is to perform on the field and hopefully that can do the talking with where I want to be,” he told espn.com.
“Gold Coast presented something that they thought would be good for me but it’s all about me preparing for 2020 and putting my best foot forward for the Cowboys.
“They’ve done a lot for me over my career, and I’m just trying to let the football do the talking. If I can perform and do my best for the team the rest will take care of itself.”
Asiata joined North Queensland in 2014 has also represented Samoa and Tonga during his career.
He is wanting to build off last season and make even bigger strides in 2020.
“I looked at 2019 as a really big stepping stone and 2020 is about trying to put myself in uncomfortable positions, trying to challenge myself and take my game and myself in general to a whole new level,” he said.
“I’m not just here to play NRL games, I’m here to try and help the club become a very well known club.
“The ultimate goal is to go to the grand final and hopefully get another premiership.”