Kelston MP Carmel Sepuloni, who was sworn in today as Social Development Minister, has been advocating to overturn the decision as the family's local MP.
Lees-Galloway said that Sepuloni's request triggered the review.
"The case file is now being prepared by Immigration NZ, which will come to us for a review of the original decision."
He could not comment on the likelihood of the decision being reversed. "We haven't seen the information."
Ultimately it will be Associate Immigration Minister Kris Faafoi that will have the authority to decide Narayan's fate.
Narayan's lawyer Alistair McClymount told Newshub that if Narayan were deported, he would be "dumped into an institution for the rest of his life".
He described the reprieve as a "positive development" and hoped Narayan would be able to stay in New Zealand.