It was reported that the world record offer from the Top 14 club has forced the World Cup-winner to reconsider his future with the Hurricanes, where he has played for more than six years.
If Barrett accepts the deal, he will become the highest paid rugby player in history, trumping Dan Carter's previous record salary of €1.4m with Parisian club Racing 92.
L'Equipe reports that fellow French clubs Stade Francais, Montpellier and Racing 92 have also made offers for the 27-year-old Kiwi.
Barrett is arguably the world's most sought after footballer as World Rugby Player of the Year in 2016 and 2017.
He scored a record 30 points against the Wallabies in Bledisloe II at Eden Park last month, which included four tries.
Barrett is off contract after the 2019 World Cup and is reportedly earning NZ$1 million a season, through his contract with NZ Rugby and the Hurricanes.
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Former All Black Lima Sopoaga — who has just moved to England from the Highlanders — stated that the appeal of wearing the black jersey is fading as more athletes are drawn to Europe by seven figure salaries.
'I do think that things are starting to change and players are starting to wise up… they realise that it's a business these days,' Sopoaga said.
'When you've got it, you've got it — but when you don't, clubs aren't going to be afraid to cut you.
'It can be pretty cut-throat; that's the way it is.'
The 27-year-old fly half — who currently plays for Premiership club Wasps — explained that a transfer to Europe can be a life changing move.
'For a lot of guys like myself, who come from big families from low socio-economic backgrounds, the chance to change your family's life is pretty overwhelming,' Sopoaga said.
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'It's not something you should take lightly.
'Sometimes the jersey is not enough for a better life.
'It is special when you do get it… but down the track, those things don't pay for a roof over your head.'
As with Australia and South Africa, NZ Rugby has a constant battle to compete with overseas riches and retain their best players.
All Blacks coach Steve Hansen wants the New Zealand government's support to help stop the trickle of departures turning into a current.
'Rugby in this country is part of who we are and what we are,' said Hansen.
'There's a lot of guys over (in Europe) who think it's a grind.
'We have to keep thinking of ways to keep this big machine going.'
Barrett is yet to comment on the L'Equipe reports.
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