Current All Blacks coach Steve Hansen is contracted through until after the 2019 Rugby World Cup but, after having been convinced to sign a two-year contract extension this year, has indicated he would be unlikely to do so again.
Hansen would have spent 16 years with the team, eight as an assistant to Graham Henry and eight in the head coaching role, at the end of his current contract.
Succession planning and continuity had been key factors in New Zealand's success in the last 13 years, in which time they have won two World Cup titles and accumulated a winning record of almost 90 percent.
Hansen's current assistant Ian Foster would therefore be a strong favourite to succeed the 58-year-old, with fellow New Zealanders Joe Schmidt (Ireland), Vern Cotter (Montpellier) and Gatland candidates, Tew said.
"Ian Foster is sitting there as a very strong candidate when Steve does finish but there'll be others," Tew told Britain's Guardian newspaper.
"Joe is sitting in Ireland and we'd like to have him back. Vern is coaching at a very high level and you wouldn't rule Gatty out either.
"(But) you'll have to ask Warren what he wants to do next."
Waikato Chiefs coach Dave Rennie, who is joining Glasgow later this year, has already said he would be interested in the role after the 2019 tournament, but was not keen on being an assistant first.
The All Blacks have already resigned themselves to losing assistant coach Wayne Smith later this year, with his replacement expected to be appointed before this year's Rugby Championship to enable them to shadow the team.
Local media have reported that Otago Highlanders assistant coach Scott McLeod, a former All Blacks centre, is a strong candidate for that role.
Tew added his organisation would begin their planning for the All Blacks direction after the 2019 World Cup later this year.
"What we will do is manage the transition very well," Tew said. "We'll be sitting down later this year to work out the process."
The Lions face the seven-times Super Rugby champion Canterbury Crusaders later on Saturday and while they had struggled in their first two games, Tew expected Gatland's side would prove competitive in the three-test series that begins on June 24.
"I'm still of the view this is a very good Lions team and once they get together they'll be very tough in this test series," said Tew.
"I think the physical attrition of the series is going to take its toll. One team will come through that better than the other."
(Reporting by Greg Stutchbury; Editing by Nick Mulvenney)
