And that rumour has come from - yes, you guessed it - France.
Rugby newspaper Midi Olympique earlier this month reported the 32-year-old outside back was likely to arrive in Pau following next year's World Cup.
The 71-test All Black and Highlanders co-captain is signed with New Zealand Rugby through to 2020.
However, he has an early termination clause in his contract next year.
It is not the first time a rumour has surfaced that Smith is heading to the French club.
Most notably, in January last year Midi Olympique suggested Smith was as good as gone.
It reported Pau had offered him a $2 million contract.
A month later, he re-signed with New Zealand Rugby and the Highlanders.
The New Zealand lifestyle was a major factor in that decision.
It was also reported this month that 24-year-old Ardie Savea could also be heading to Pau.
The Hurricanes and All Black flanker would join brother and former All Black Julian in France, the 28-year-old linking with Toulon this year.
Savea is signed with New Zealand Rugby through to 2019, although he did not extend his contract.
Pau is coached by Simon Mannix, while fellow former All Blacks Carl Hayman and Conrad Smith are his assistants.
Its playing roster is also filled with Kiwi ex-pats.
Former All Blacks Tom Taylor, Frank Halai, Colin Slade, Benson Stanley and Jamie Mackintosh are all with the side, as is ex-Otago lock Daniel Ramsay.
Regardless of whether Smith and Savea leave, it would not be a surprise to see several All Blacks head offshore after the World Cup.
The list of players coming off contract after the World Cup includes Kieran Read, Beauden Barrett, Brodie Retallick, Sam Whitelock, Dane Coles, Owen Franks, Joe Moody, Liam Squire, Aaron Smith, Sonny Bill Williams, Jordie Barrett and Waisake Naholo.