Palenski said Snell's wife Miki phone him this morning to share the sad news.
The couple had been planning to go out shopping on Thursday noon Dallas time, when Snell "nodded off to sleep".
"Miki was getting ready, and Peter nodded off, as is not unusual for him. But he didn't wake up."
Snell was 80, and due to turn 81 on Tuesday.
Snell is one of New Zealand's most famous Olympians – winning three gold medals (in the 800m at the 1960 Rome games, and then in both the 800m and 1500m in the Tokyo games).
Born in Taranaki, his family later moved to Waikato, before he completed his schooling at Mt Albert Grammar.
By the age of 19 he was concentrating on athletics.
Palenski, chief executive of the New Zealand Sports Hall of Fame, was a friend of Snell's and had worked with him a lot over his career in his journalism and writing.
"It is very sad news, a grievous loss for New Zealand."