Luai, who was part of NSW’s Origin II triumph on Sunday, has previously represented the Pacific nation.
Samoa are in the midst of a coaching crisis with Matt Parish and the nation’s board off-side with a number of leading players, including Luai and Queensland’s Josh Papalii.
Luai has in the past indicated he wanted to help Samoa mirror the growth of Tonga on the international stage, but Meninga encouraged the Penrith five-eighth to change his allegiance.
“Josh is now 31 and he’s at the back end of his career, and he’s earned the respect and right to choose who he wants to play for,” Meninga told the Sydney Morning Herald.
“But Jarome is at the start of his career and I’d like to think he will make himself available for Australia.
“I’ve made it known in the past if a player can play Origin, they should then make themselves available for Australia.
“I’m keen to speak with Jarome and let him know what my feelings and thoughts are about the international game.
“I’m also keen to hear his thoughts and reasons for wanting to play for Samoa. I can tell you he’s absolutely in the mix for Australia.”
The Origin eligibility rules allow forbid players from playing for a tier-one country over than Australia, but do allow players to turn out for NSW or Queensland and then represent a tier-two nation such as Tonga or Samoa.
Luai, like Papalii, has previously indicated he wants to return and play for Samoa if there is a change of coach.
“We have the potential to go really far. One of my goals is to get a really strong squad for the next World Cup,” Papalii told foxsports.com.au.
“There are some pretty big names who are keen to jump on board and help Samoa be where they should be.”