The Ukrainian's handlers insist that Germany's National Anti-Doping Agency (NADA) handle any drug testing, but Povetkin's camp want to use the Russian agency.
Should the German agency not be used, "there will be no fight and this is not up for discussion," Klitschko's manager, Bernd Boente, said at the weekend.
Boente said Povetkin, 33, must also have his samples tested by the NADA-certified institute in Cologne.
The Klitschko camp want to "rule out any inconsistencies with questionable analysis by Russian anti-doping agencies" before the fight goes ahead.
"Better safe than sorry. I've already seen too much in this business," said Boente.
Heavyweight champion Klitschko, 37, has been ordered by the WBA to face the Russian in Moscow on October 5.
Povetkin is the WBA “regular” champion and Klitschko the “super” champion; an honour given to him after he beat Britain's David Haye in a fight for the WBA belt in July 2011.
Now Klitschko, who also holds the WBO, IBF and IBO belts, and Povetkin are obliged to fight to leave just a single WBA champion.
The WBA have granted a seven-day extension for the fight's details to be negotiated. “There are still huge gaps in the contracts, not only in terms of the drugs testing," admitted Boente.
Russian promoter Vladimir Hryunov won the race to stage the bout with a staggering $23.33-million bid.
Klitschko is entitled to 75 per cent, which would give him a career-high $17.3-million purse. Povetkin should receive $5.7 million.
The former Olympic Games champions were due to clash twice before but Povetkin pulled out in 2008 because of injury and then backed out a second time in 2010.