French sports newspaper L'Equipe said on Thursday that Racing president Jacky Lorenzetti and Bath owner Bruce Craig have agreed the transfer.
Paris-based Racing are now said to be awaiting 30-year-old England international Barkley's answer, although there has been no official comment from either club or the player himself.
Barkley, who has won 23 caps but does not feature in the current England Elite or Saxons squads, has started the Aviva Premiership season impressively for Bath.
They have won two of their first three games, with fly-half Barkley's goal-kicking an integral part of victories over Worcester and Wasps.
He would answer an injury SOS for Racing less than a month from launching a Heineken Cup campaign that sees them in the same group as Saracens, Munster and Edinburgh.
Juan Martin Hernandez is currently on Rugby Championship duty with Argentina, while two other number 10s - Jonathan Wisniewski and Benjamin Dambielle - are nursing long-term injuries.
Barkley is in his second spell with Bath after rejoining them from Gloucester in 2009.
His latest spell at the Recreation Ground has seen him suffer a broken leg on two separate occasions, but he is now fully fit and had appeared to be a key part of a squad under the coaching direction of South African Gary Gold.
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