The announcement is said to be due on March 15 with the device going on sale shortly afterwards.
The report comes originally from technology blog 9to5Mac, with Apple offering no confirmation.
The new ‘iPhone 5se’ with a four inch screen is supposedly aimed at people who want faster phones using the Apple operating system without having to upgrade to the far larger iPhone 6s and 6s Plus.
This comes amid a trough in demand for the device. A 0.4 percent rise in shipments in the fiscal first quarter was the slowest-ever increase in iPhone sales since the phone was launched in 2007, though that is partly linked to people waiting for the release of the rumoured iPhone 7, expected in September.
A new iPad Air is also reported to be set for launch on March 15 as the company tries to revive slumping sales of its tablets.
The device, with a 10.1-inch screen, will reportedly have some of the features that first appeared on the iPad Pro,including improved speakers.