Foxconn is reported to be assembling 150,000 iPhone 5s every day, according to reports.
Digitimes claims that shipments could reach six million in September, citing industry sources.
"Lens maker Largan Precision, touch panel maker TPK Holding, reinforced glass supplier G-Tech Optoelectronics and battery vendors Simplo and Dynapack are all operating at full swing currently, the sources indicated," according to Digitimes.
Shipments of the iPhone 5 in the fourth quarter could reach 22 million units, but Pegatron, the other company that Apple has engaged to assemble the next-generation iPhone, may not begin shipping units until 2012, the report added.
Earlier this week, it was reported that both Foxconn and Pegatron had begun assembling the iPhone 5, though were not boxing the units as iOS 5 was not ready for installation.