The Fiji-born winger has openly admitted he would consider a switch in a bid to get the best deal for him and his family.
Wife Rebekka is also disillusioned with the amount of time her husband spends overseas away from their young son
Samson, and would welcome his swift return to the NRL.
"It can be quite alarming to see how much time he is away and they're kept to themselves quite a bit," she told the Courier Mail.
"There's not much opportunity for families to be accommodated too much in the travel."
Tuqiri, who played 99 games with the Brisbane Broncos between 1999 and 2001, has already held talks with his former club as well as Cronulla and Sydney Roosters.
And although the Australian Rugby Union has offered Tuqiri a lucrative four-year deal, he has expressed his disappointment with the financial aspects.
"It wasn't quite up to the mark of what we thought I'm worth," Tuqiri told Channel Nine.
"That goes back to a lot of things, and the ARU know about that."
ARU boss Gary Flowers was unhappy with the winger's comments, but the organisation is unlikely to give up on Tuqiri without a fight.
"We communicated our view and while I'm not going to canvass what was said, it's fair to say we weren't feeling overly positive," Flowers said.
Tuqiri captained Fiji in the 2000 Rugby League World Cup before being selected for Australia in 2001, when he debuted with a try against New Zealand in a 28-10 victory.
He switched codes the following year where he joined the NSW Waratahs, and made his international debut for the Wallabies in 2003 against Ireland.