Carter missed Racing's 15-12 defeat to Leinster in Bilbao due to a hamstring injury but could be fit to face either Toulouse or Castres in Lyon on May 26 in the Top 14 semi-final, according to backs coach Laurent Labit.
If not available in two weeks' time, Carter, who will leave the French side for Kobelco Steelers in Japan at the season's end, is "sure" to be fit for the June 3 final in Paris, Labit said.
Ireland international lock Donnacha Ryan, who injured a shoulder against Leinster, is likewise facing a race against time for the Top 14 semi-final but looks otherwise certain to return to full fitness ahead of the final.
However, the news on South Africa international fly-half Pat Lambie is not so good.
Lambie is waiting to see a specialist to find out if he has ruptured his cruciate knee ligaments, an injury that forced him off the field against Leinster after just three minutes of Saturday's European Champions Cup final.
Lambie himself said after the match he thought his season was over.
Racing are already without France scrum-half Maxime Machenaud, full-back Brice Dulin -- both of whom have ruptured cruciate knee ligaments -- and hooker Dimitri Szarzewski, who has a biceps injury.
Racing have a bye into the Top 14 semi-finals after finishing in the top two in the regular season, alongside table-toppers Montpellier.
This weekend Toulouse take on Castres and Toulon play Lyon for the final two places in the semi-finals.