The match is not a formal part of the £225m agreement with the RFU.
The All Blacks have a hectic year including hosting the British and Irish Lions, but have been keen on a fourth match on their end of year tour north.
England and New Zealand last clashed in 2014, with the All Blacks winning a three Test series at home 3-0.
England have not played the All Blacks during their golden run under coach Eddie Jones and are not officially scheduled to meet until late next year.
Further obstacles are presented by the need to negotiate with the Aviva Premiership clubs for player release and concerns over player welfare that will accompany any decision to add the All Blacks to an autumn fixture list that already includes Australia, Argentina and Samoa.
England are not due to face New Zealand until 2018 but a meeting earlier would generate worldwide interest and potentially £12m for the Rugby Football Union from gate receipts, sponsorship and hospitality.
Premiership Rugby said on Wednesday they had yet to be consulted regarding the fixture.
England are dominating the northern hemisphere and have equalled the All Blacks' world record of 18 consecutive tier one test wins.
The south west London stadium looked likely to be the venue for a match between the All Blacks and the Barbarians on that date - a contest that had been provisionally agreed to - but according to a report published to The Daily Mail website on Tuesday, RFU chief executive Ian Ritchie is hoping to push the "Baa-Baas" out of the picture and put together a much more significant showdown between the world's two highest ranking worldwide sides.
They get the chance to claim the mark for themselves when they play Ireland in the Six Nations finale in Dublin this weekend.
"If there now might be an opportunity to play them this year, we want to pursue it", the statement read.
Jones replied by expressing his wariness of Hansen's approval, noting that compliments from an All Blacks coach are akin to fairytale predator the Big Bad Wolf stalking Little Red Riding Hood.
"We want competition and games that people want to watch and get excited by", Hansen told the BBC's Sportsweek programme. I think the thing that made it hard was perhaps we didn't play as well as we could as a team.