Waqa, who was a member of Melbourne's 2012 premiership-winning team, will take the number of Fijians in the NRL to 23 if he can convince Storm coaching Craig Bellamy to sign him after a stint with French rugby union club, FC Grenoble.
The 31-year-old recently returned to Melbourne, where his family had been living, after breaking his jaw and was offered a training contract with the Storm.
Melbourne football director Frank Ponissi said a decision would be made on whether to sign Waqa before June 30 so he is eligible to play the remainder of the season.
"He got injured just before Christmas and moved back about three weeks ago," Ponissi said.
"We will have a look at him over the next few weeks and if he comes up all right we will sign him for the rest of the season.
"He is still a fair way off playing because he has been inactive for a while but he is showing good signs. This is his second week of training and we will probably give it another two weeks before we make a call.
"I'm sure he will come into consideration for the Fiji side at the World Cup if he does sign for the rest of the year."
While he played most of his 95 NRL matches for the Roosters, Storm and Raiders on the wing, Waqa would offer the Bati versatility in the backline as he was considered a star five-eighth as a rugby union schoolboy in Fiji and modelled his game on former Wallabies great Stephen Larkham.
He played one rugby union Test for Fiji in 2007 before switching codes to join Sydney Roosters in 2009.
Waqa has also played centre for the Bati, who he represented at the 2013 Rugby League World Cup and in last year's Melanesian Cup against Papua New Guinea.
The signing of Waqa would take the Storm's Fiji representation to three, along with star winger Suliasi Vunivalu and prop Tui Kamikamika.
In total, there are 25 players eligible for the Bati who are currently playing NRL, including Fiji rugby sevens Olympic gold medallist Masivesi Dakuwaqa, who scored a try for Canberra's NSWRL feeder team, Mounties, in his first game after joining the Raiders last week.
Korbin Sims (Broncos)
Masivesi Dakuwaqa (Canberra Raiders)
Marcelo Montoya, Tyrone Phillips (Canterbury Bulldogs)
Jason Bukuya (Cronulla Sharks)
Jarryd Hayne, Ben Nakubuwai (Gold Coast Titans)
Apisai Koroisau, Akuila Uate (Manly Sea Eagles)
Suliasi Vunivalu, Tui Kamikamika, Sisa Waqa (Melbourne Storm)
Daniel Saifiti, Jacob Saifiti (Newcastle Knights)
Semi Radradra (Parramatta Eels)
Waqa Blake, Campbell Regan-Gillard, Viliame Kikau (Penrith Panthers)
Tariq Sims, Taane Milne (St George Illawarra Dragons)
John Sutton, Sitiveni Moceidreke (South Sydney Rabbitohs)
Kane Evans, Eloni Vunakece (Sydney Roosters)
Kevin Naiqama (Wests Tigers)
Photo: NRL (Former Roosters, Storm and Raiders winger Sisa Waqa is eyeing a return to the NRL and the Fiji Bati at the 2017 Rugby League World Cup).