Smith, who was assistant to Graham Henry for eight years and helped guide the All Blacks to World Cup victory last year, has been strongly linked to a role with England under new coach Stuart Lancaster.
Smith, who coached Northampton in the English top division from 2001-2004, has taken a coaching role with the Super Rugby Waikato Chiefs, helping guide them to the top of the table, and said he had met Lancaster when the Chiefs were in South Africa recently.
NZRU chief executive Steve Tew, however, said the organisation would do everything they could to ensure they keep Smith in the country.
"We consider Wayne to be an incredible asset to New Zealand rugby, not just the All Blacks but New Zealandrugby full stop," Tew told reporters after a NZRU board meeting.
"He has worked incredibly hard on behalf of this organisation for an extended period of time so he has earned our respect to make whatever decision he wants to make and we are certainly not going to leave him without options, but we are desperately keen to keep him in New Zealand."
The 55-year-old former All Blacks flyhalf held immense knowledge of how the team operated, their tactics and coaching techniques, Tew said, and the organisation would be keen to hang on to that.
"He is one of our intellectual properties. He has been with us for so long and been such an important contributor to developing things that work in our environment that we think he is a special case to protect.
"He has achieved an enormous amount as a coach and he loves coaching and he loves a challenge ... we are dead keen to find a solution but there is no easy one."
Smith told the New Zealand Rugby Union website (www.allblacks.com) on Friday he had been offered a hands on role with the England team, with Lancaster adopting a director of coaching role in order to plan the strategic direction of the team and liaising with the clubs.
Smith has an exit clause in his Chiefs contract and if he were to leave New Zealand, it would probably not be until the end of the current Super Rugby season in August.
The All Blacks have an end of year tour to Europe with a match scheduled against England on December 1, and Smith said that could be a factor in his ultimate decision.
"Having put the last eight years of my life into coaching the All Blacks and trying to win the World Cup, I'm going to have to search inside myself to see whether I could coach a team against them," Smith said, adding he hoped to make a decision over the next 10 days.
"It's not just going to any team, it's going to a team that over time will potentially challenge the All Blacks, so I've got to be clear in my mind that I could be a part of that."