David Bain's lawyer wants his client's relatives to be "generous" and give him back an inheritance that, he says, is legally his.
Mr Bain's family owned a house in Every St, Dunedin, which was burned down just weeks after his parents and three siblings were shot dead in June 1994.
The Bains also owned a section in Whangarei and another in Bundaberg, Queensland.
They had about $60,000 invested with friends and a substantial amount in an overseas bank account, the Press reported.
Mr Bain was initially convicted of the five murders and received nothing from the sale of the properties, to prevent him from benefiting from the proceeds of crime.
His lead QC, Michael Reed, says he hasn't heard from the family yet "but I'm hoping they might wish to make that gesture to David - he's got no money after all".
"It would be a very nice gesture if the family gave him the money that originally lawfully belonged to him and was taken from him only because he was convicted."
Some of the extended family gave evidence for the Crown at the retrial but Mr Reed said, despite that, he hoped they would still be generous.
The relatives who acquired all of Mr Bain's inheritance after his original conviction were refusing last night to be drawn into arguments over the return of his money.
Mr Bain's paternal uncle, Michael Bain, would say only: "I will reserve comment on the matter."
He would also not reveal his feelings about Friday's not guilty verdict or whether the family would have anything to do with Mr Bain.
Asked how his family had coped through the ordeal, he said, "Fine, thanks."
Valerie Boyd, sister of David's mother Margaret Bain, would also not comment when contacted by the Herald yesterday.
She had earlier told the Herald on Sunday: "We need time."
Mr Bain's chief supporter, Joe Karam, would not elaborate on whether his legal team would vigorously pursue the inheritance.
The former All Black said he was looking forward to moving back to Te Kauwhata in northern Waikato, where Mr Bain was likely to join him for a while.
"David will certainly be coming to stay with me but it certainly isn't a long-term plan.
"He will certainly be coming to spend some relaxation time with me in Te Kauwhata and obviously over that period of time he will make some plans."