Hansen announced in Auckland on Friday morning that he will step down following the 2019 Rugby World Cup in Japan.
If New Zealand Rugby maintains the policy of promoting from within that it adopted when appointing Hansen, then Foster will be favourite for the top job.
Hansen's decision could lead to Joe Schmidt taking over as New Zealand coach.
All Blacks Beauden Barrett and Rieko Ioane, and Black Ferns skipper Fiao'o Faamausili are finalists for the men's and women's 15s Player of the Year awards for the 2018 World Rugby Awards.
Asked if Hansen could now instead take up a more senior role, he explained: "Whenever you lose someone who's been around for a long time, there's a desire to (a) protect what they know and make sure it doesn't go somewhere else and (b) to make sure that we transition".
"Fiao'o, Beauden and Rieko bring our total number of nominations for the awards to seven, with Black Ferns Sevens players - Sarah Goss, Portia Woodman and Michaela Blyde nominated for the Women's Sevens Player of the Year award, and All Blacks prop Karl Tu'inukuafe nominated for Breakthrough Player of Year".
The win comes after last year's effort from the Black Ferns, who beat out the All Blacks for the 2017 Team of the Year.
"This is a critical process which shouldn't be rushed and shouldn't be made in the turbulent period that tends to follow a Rugby World Cup campaign", he said.
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Yet prior to that he said he felt it was better if a coach stepped down mid-way through a World Cup cycle with his successor having been part of the team's set-up.
That defeat to Ireland hinted at a potential power shift in worldwide rugby, with Joe Schmidt's side a serious contender to win next year's World Cup.
However, Gatland is believed to have a frosty relationship with New Zealand Rugby's upper echelons and his appointment would come as a surprise, despite his impressive record. It could happen, though probably not next year.
"I'm highly motivated by that, as is the whole group, and we're really looking forward to it", Hansen said.
Scott Robertson has revived the Canterbury Crusaders with two titles in his first two seasons in charge and before that he won three titles in four years in the domestic competition.
"He's hugely respected, clear in his views, and will leave the job as one of the greatest ever All Blacks coaches", Impey said.
Other Kiwi coaches considered outside chances to replace Hansen include Jamie Joseph, now coaching Japan, Glasgow Warriors mentor Dave Rennie and Vern Cotter at Montpellier.