In an interview with The Wall Street Journal, Trump said Cook had promised him that Apple would build “three big plants, beautiful plants", but did not specify where or when the plants would be built.
Apple has about 80,000 employees in the US and the company says it supports about two million jobs in all.
Last year, during the presidential campaign, Apple was criticised by Trump for outsourcing its manufacturing to factories in China.
The WSJ said that a small proportion of Apple's products are made in the US on contract. Flex makes Mac computers in Austin, Texas, and Quanta Computer makes Macs in Fremont, California.
However, most Apple products are assembled in China, mainly by Foxconn Technology, which makes the iPhone and a number of other products.
Trump also said that Foxconn had plans to build a big plant in the US and was thinking of locating it in Wisconsin.