Zheng's doubles partner Yan Zi will also skip China's world group debut in Castellaneta Marina on April 21-22 to make way for Peng Shuai, Olympic doubles gold medallist Sun Tiantian and "some youngsters with potential".
"This is to ensure the Olympic players have played Fed Cup twice before the Games as the (rules) require," Gao Shenyang, deputy director of the CTA, told Reuters in an interview.
"The Olympics has the first priority," he added. "If there are conflicts we have to sacrifice the Fed Cup."
Li is China's best hope of singles gold at next year's Olympics and Gao said the CTA were still looking for another coach for the world number 17.
"Li Na is a very talented player and we'll offer her more help and support," he said.
"We're now looking for a top class foreign coach and before that we let her husband coach her temporarily. So far we have seen positive effects.
"We've hired experts to strengthen her physical power and a team of researchers is analysing her every match and reporting back to her coach."
FRAGILE MENTALITY
Two sports psychologists have also been recruited to help the women players but Gao said he thought Li's shortcomings were as much technical as the result of her fragile mentality.
"She has a strong forehand attack but a lack of variety and is weak in net play," he said.
"So if the opponent withstands her first attacks... she becomes impatient. It is not simply a mental problem."
Gao said that contrary to internet rumours, Zheng and Yan, who won the Australian Open and Wimbledon doubles last year, would not be split up in the shake-up of women's doubles partnerships.
"They have encountered some new problems and new challenges and they are positively reviewing them and trying to find ways of progressing," he said.
"We are also trying out new pairings and will fix the second and third doubles before June and start to get points for the Olympic qualifiers."
Gao also said negotiations were continuing for former French Open champion Michael Chang to coach China's number three Peng.
The Chinese-American spoke to the CTA about helping out on a visit to China last November and was pictured watching world number 40 Peng playing at the Sony Ericsson Open in Miami last week.
"Personally I very much hope we can sort it out," Gao said.
(Additional reporting by Liu Zhen)