Lowe was part of the Ireland side that beat the All Blacks 2-1 in the Steinlager Series at the weekend.
Dagg said he visited the Leinster headquarters during the All Blacks northern tour in 2016.
"I was really close to signing for Leinster. What stopped me from signing was it was so cold! It was freezing. I'm from Christchurch, where it's very cold, but that place is on another level.
"I went to the Leinster headquarters with Isa Nacewa and saw the whole complex. I loved it. I had to try to convince the wife, she was obviously a big part of it. She said no," he told the42.ie.
"I turned the deal down, came back to New Zealand, and they actually gave my contract to James Lowe," he said.
Dagg said he was proud of what Lowe achieved with Ireland.
There were moments when Dagg wondered what might have been had he signed with Leinster.
"I never really got to experience anything outside of New Zealand. I went to Japan for two months towards the end of my career, but my knee was very bad. I couldn't really play, I was just not in a happy place, my body was breaking down," he said.
"I never got to understand what rugby means to other nations and what it means to different players. And how good would it have been playing with world-class players in Ireland, or in England, or whatever.
"But in saying that, I had a pretty special career. I started when I was still at school playing for Hawke's Bay, playing the grades, and to experience what I feel was a golden era in New Zealand rugby.
"I got to play with the greats of all-time, Richie McCaw, Dan Carter, Kieran Read, Ma'a Nonu, Conrad Smith…the backline was freakish. So I pinch myself, but I would have loved to have gone and experience a different culture," he said.