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French news outlet Midi Olympique suggested the French Rugby Federation was close to signing an agreement with New Zealand Rugby for a second match in addition to the November 12th test in Paris.
New Zealand Rugby boss Steve Tew has told Sky Sport they won't be playing France, but another team remains a possibility.
"We won't be playing France midweek in a test match in France but the coaches are looking for additional matches in a softer environment if you like," he told The Breakdown last night.
"The Barbarians game has been added to the schedule and we are looking at another possible game, midweek in France, but work is still to be done."
That suggests a clash against the likes of Top 14 sides Toulon, Racing or Montpellier could be on the cards.
Marseille has been suggested as a possible location by French media however the city doesn't have a team in France's top division. Top 14 teams Toulon, current club of former All Blacks second-five Ma'a Nonu, and Montpellier play not far from Marseille.
Another other option would play a Paris-based club since the All Blacks will already be based in the French capital.
No doubt All Blacks fans would like the prospect of New Zealand coming up against Dan Carter and Racing.
The FFR were originally keen to host a second match against Steve Hansen's side on Saturday 4 November, but that date has already been taken up by the All Blacks' clash against the Barbarians at Twickenham in London as a celebratory fixture for NZR's 125th anniversary.
A fifth match on tour would add a massive amount pressure on the All Blacks, who would still have to face an impressive Scotland side in Edinburgh on 18 November before finishing their season against Wales in Cardiff a week later.
All these matches would come at the end of a season where the national side would have already played a test series against the British and Irish Lions in addition to a potential warm-up test against Samoa in June, as well as partaking in the annual Rugby Championship competition against Australia, South Africa and Argentina.
Although an additional match in an already prolonged season for the All Blacks would place a lot of physical and mental pressure on members of the squad, it could give Hansen an opportunity to blood newcomers and test the depth of his player pool as he eyes a third consecutive World Cup title in 2019.
End-of-year tours usually allow young players to showcase their talent, and the match against the Barbarians and a second fixture against France would give Hansen plenty of opportunities to give his unproven players a chance to show their worth halfway through the World Cup cycle.