The 31-year-old loose forward is reportedly top of Racing's shopping list and they are prepared to pay top dollar.
Savea is contracted to New Zealand Rugby through to the end of 2027 but the French club is keen to get in early and grab his signature.
According to The Daily Telegraph in Australia, Racing are willing to make him the "highest-paid player in rugby history", eclipsing the deals handed to Dan Carter and Matt Giteau in Japan.
Savea, the 2023 World Rugby 15's Player of the Year, played Super Rugby for Moana Pasifika this past season.
He will head to Japan next season on sabbatical with the Kobelco Kobe Steelers, before returning to New Zealand in 2027.
In recent years, Paris 92 have signed players such as Springboks captain Siya Kolisi and English star Owen Farrell.
Carter headed to France to play for Paris 92 after winning the World Cup in 2015.
He spent three years there before moving to Kobelco Steelers in 2018.
Savea has played 99 tests for New Zealand.
