Asofa-Solomona first explored the possibility of a code defection last month when he met with Wellington hierarchy during the NRL Nines tournament in Auckland.
Off-contract at season's end, Asofa-Solomona has yet to formally sign with NZR but it is understood the Hurricanes will trump the Storm in the battle for his signature.
Melbourne's hopes of retaining the front-row wrecking ball will not be aided by the fact he has started the season with Queensland-based feeder-club Sunshine Coast in the Intrust Super Cup.
Asofa-Solomona's mother, Ailini, confirmed New Zealand rugby bosses were circling as her son weighs up his NRL future.
"Nelson is a rugby boy so he knows the game well. We won't stop him if he wants to come back to rugby," she told The Courier-Mail from her home in Wellington.
"That's a dream for any young kid growing up in New Zealand, the aim for Nelson is to be in the All Blacks, but I'll support what Nelson wants to do.
"Wellington are trying very hard to sign him. They want him to come back and they said the door will always be wide open whenever he decides to come back. It (returning to rugby) is always in his mind. He knows how much we want him to be in the All Blacks team but we'll support whatever he does."
Asofa-Solomona has also been sounded out by New Zealand Sevens coach Gordon Tietjens on the eve of the 2016 Rio Olympics.
Storm coach Craig Bellamy has a huge opinion of Asofa-Solomona but started him at the Sunshine Coast this season to help improve his error-rate in games.
Ailini said her son has enjoyed his stint at the Storm but is battling homesickness.
"The interest from rugby in him over here is crazy," she said. "Nelson is contracted to the Storm this year but he gets homesick, he wants me to ring him all the time.
"I tried to help him settle down, I was living with him for three or four months in Melbourne when he joined the Storm but then I moved back here. I'd love to see him come home, but it's up to Nelson and what he wants to do."
- news.com.au
