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The Rugby Paper reported that both clubs were keen to secure Carter's services when he takes his sabbatical before the next Rugby World Cup.
The British publication is reporting that Racing Metro president Jacky Lorenzetti has been in talks with Carter's agent and is offering him a 4-million pound, three-year contract after the 2015 World Cup.
Toulon's multi-millionaire owner Mourad Boudjellal has also entered the bidding war.
A source told the Rugby Paper: "Boudjellal has been in contact with Dan's representatives so it will probably come down to a bidding war between them and Metro.
"Metro really want to bring him over and, what they have in their favour is that, Carter is set to have a young family and Paris would be very attractive in that regard."
Carter signed a four-year contract with the New Zealand Rugby Union before the 2011 World Cup with the option of a second sabbatical in it.
He was the first player to be granted dispensation to play abroad as part of his contractual agreement with the NZRU.
He went to Perpignan in 2009 but managed only four games before he seriously damaged an Achilles tendon.
He retained a sense of unfinished business from his French sojourn but is close to turning 31 and the dangers of returning to the highly physical French league in 2014 would be considerable.
The indications at this stage are that Carter will most likely be available for all of next year's All Blacks programme but then possibly play in Japan from December 2013 through to February 2014 and not return to Super Rugby until after the June test window.
The Japanese league is not known for its physicality, and its shortness would provide Carter a nice overall mix in a six-month sabbatical - a change of scene where he would be well paid and able to focus on aerobic improvements and then a period of prolonged rest.
The other option would be for Carter to follow Richie McCaw's example and simply take a break from all rugby in the first six months of 2014.
Whatever he decides, it would seem the one thing not likely to happen is him being available for all Super Rugby commitments between now and the World Cup.