Smith was one of New Zealand's "three wise men" - along with Graham Henry and Steve Hansen - who guided the All Blacks to their World Cup triumph in Auckland last October.
Lancaster met with Smith, the former Northampton director of rugby, over dinner in Durban last Friday night to discuss the role and to sell his vision for the future of English rugby.
Smith was impressed and he is now considering the offer of a role as part of England's own "three wise men" management team, alongside Lancaster and Graham Rowntree.
"(I had to) find the Andy Farrell replacement, look around to see who was the best person for that fit. For me, there is one stand-out candidate - Wayne Smith," Lancaster told BBC Radio 5 Live.
"I met him and had a real good chat with him. He has some decisions to make of his own.
"Clearly the lure of international rugby is a strong one for him. He enjoyed his time at Northampton, he enjoyed his time in England.
"He was excited by the vision I presented to him about where we were going as a national team."
"Wayne has got not just a lot to offer from a coaching point of view, in terms of experience, southern hemisphere and he has been in World Cups. It was a really, really enjoyable conversation."
Smith left the meeting excited by what he heard and he believes Lancaster can turn England into a side capable of challenging New Zealand's supremacy and winning the 2015 World Cup on home soil.
But before he is in a position to accept the job, Smith has to come to terms with the prospect of severing ties with the All Blacks and coaching directly against the team he helped guide to World Cup success.
England play New Zealand at Twickenham on December 1 and Smith foresees an intense rivalry developing between the two nations over the next three years.
"It is possible (I could coach England against the All Blacks). I have to search inside myself to see whether I can do that or not," Smith said.
"I am patriotic and I love the All Black jersey. That is why it is such a big decision.
"They (England) are a team on the up with a lot of resources. I was very impressed with Stuart Lancaster. He has a clarity of vision that I think will make a difference up there.
"I think they will be a tough proposition over the next few years."
Lancaster rebuilt English rugby following the disastrous World Cup campaign, pulling together a new team with a new ethos and guiding them to second place in the Six Nations.
Smith recognised similarities between England's recent development and the job he inherited with the All Blacks after the 2003 World Cup.
"I talked about the history and the journey from the end of the World Cup 2011 through to the end of the Six Nations," Lancaster said.
"He talked a lot about how that reminded him of New Zealand in 2004 and how a new leadership group emerged, a new group of players emerged. They got across the line in 2011.
"We had a really good conversation about that. He could resonate with where we were going. He could see we were prepared to give young players a chance, that we were prepared to play and give that no fear approach to players.
"International rugby is hugely exciting. Let's not die wondering."
Even if Smith can be persuaded to leave New Zealand, where he has strong family ties, he will not be available until after England's summer tour of South Africa.
Lancaster confirmed he has held talks with Mike Catt over the interim role, with a decision to be finalised next week.
Former Wasps fly-half Alex King had also been under consideration but his commitments with French club Clermont Auvergne, whose season may not finish until June 9, ruled him out of contention.
Lancaster denied suggestions Smith would be the head coach in a new England set-up, insisting there would be no change to the integrated structure that existed with Farrell in the Six Nations.
"I am more for an integrated approach, where everyone contributes in each other's area but there is accountability," Lancaster said.
"My role is to work with the commercial teams, the media, the directors of rugby in the Premiership, the RFU.
"It's a wide-ranging role but equally it's a coaching role as well and I will set the overall framework of how we are going to play and then the coaches would work on that detail.
"When Andy, Graham and I worked together I would set the basic framework of how we would play. It was always an integrated approach.
"Andy would lead on defence but he would have a view on attack and he would coach the set piece attack in the backs and the kicking game.
"Graham would lead on the forwards and he would be involved in defence and some of our attacking options off scrums and lineouts.
"The role for Wayne is the same as what Andy did."