All Blacks coach Steve Hansen is set to step down after Friday's third-place match against Wales in Tokyo after the two-time defending world champions were stunned by England in the semi-final.
Gatland is also poised to depart Wales following 12 years in charge as he prepares to coach the Lions in South Africa in 2021, while he has also signed on to lead Super Rugby outfit the Chiefs on a four-year deal.
Tew, who will also vacate his position at the end of the year, poured cold water on the prospect of the 56-year-old New Zealander replacing Hansen.
"I don't know that he is going to apply for the job or not," Tew told New Zealand's Radio Sport on Monday. "He knows what our process is. He's made those decisions already, what he has in his contracts in terms of what he's going to do is entirely up to him.
"I haven't actually contemplated this but I think to coach the All Blacks and the Lions in a four-year period would be impossible but that would be a call that he has made or that he will have to make."
Tew added: "Nothing has changed from the original process, with the semi-final result no need to accelerate the decision, it is important that we focus on that, win or lose this was always the process."
Photo Getty Images Caption: Warren Gatland