Users outside the U.S. are reporting that the service is intermittently appearing on their iPhones and other Apple devices.
According to Apple Insider, so far consumers in the U.K., Canada and Australia have claimed that the Internet radio service is cropping up on their devices, though the functionality is limited.
Announced in June 2013 and initially launched in the U.S. in September, iTunes Radio lets users listen to an Internet radio station of tracks complied by artist, genre or theme. The service is free when supported by ads or, for consumers who already pay to use iTunes Match -- the cloud-based music storage, streaming and matching service -- it is both free of extra cost and free of ads.
Though Apple does intend to offer the service beyond the U.S., it is yet to set any time or date on when consumers can expect it to arrive in their countries.
Nevertheless, sources have claimed that Apple's intention with the service is to roll it out in the U.K., Canada, Australia and New Zealand early this year.
Music streaming services are expected to be one of the key tech battle grounds of 2014. Earlier this month, Beats Music launched (in the U.S. only), and it has been so overwhelmed by take-up that it has had to close the service to new users and introduce a waiting list while it strengthens its platform to cope with demand.
YouTube is also hotly tipped to launch its own music streaming service, which would serve up videos as well as tracks later in 2014.