Samsung said it would probably reach that sales milestone next week, even though the S4 has been on sale for just a month.
"It is selling much faster than the previous model S3," Shin Jong-kyun, Samsung's co-chief executive, said in Seoul.
Last year's Galaxy S III was also quick to hit the 10-million mark although it took two full months, the Los Angeles Times reported.
Total sales of the S III have reached 50 million, Samsung said.
The popular S4 smartphone, available in the United States from AT&T, Sprint and T-Mobile and coming to Verizon next week, is likely to be Samsung's fastest-selling smartphone of all time, the Times said.
The Galaxy S4, on sale in more than 60 countries worldwide, features a 5-inch display, a 13-megapixel camera and 4G LTE service.