In a new report from DigiTimes, Taiwanese memory module makers said there have been a “serious shortage” of NAND flash chips, as companies provide more and more of their supply to Apple. Industry sources said memory providers will limit the supply of memory provided to companies other than the Cupertino, Calif., hardware maker.

“Samsung Electronics has informed Taiwan module makers that it will halve its NAND flash memory to them in September, and Micron Technology has also told some of its downstream customers that no NAND flash chips are available, claimed the sources,” the report said. “Toshiba and Hynix Semiconductor are also giving priority to Apple, and are offering limited supply to the spot market, the sources added.”

The average price for a 16GB chip was $4.48, up 7.2 percent in the first half of September. 32GB also rose 4.3 percent to $6.80.

Last week, Apple unveiled a new 64GB iPod touch for $399, doubling the capacity of its previous highest capacity 32GB model. In addition, this summer the 16GB and 32GB iPhone 3GS models were introduced.

As Apple has continued to double its available capacities on the iPhone and iPod touch every year, competitors have struggled to keep up. This week Microsoft will release its new Zune HD, available with flash memory capacities of 16GB and 32GB.

If true, the latest report from DigiTimes could suggest that competitors, like the Zune HD, have been unable to offer the capacity of the iPod touch because memory suppliers simply will not provide enough product to anyone other than Apple.