Analysts at Nomura said Nokia, which has led the market for 14 years, will be pushed into third place later this year by Apple.
Even that position looks likely to be challenged by Korean firm HTC during 2012, analysts said, "further emphasising the shift in power to Asia".
Nokia, which created the smartphone market with its 1996 launch of its Communicator model, has lost initiative to Apple's iPhone and Google's Android devices, and at the lower end to more nimble Asian rivals.
Led by new chief executive Stephen Elop, Nokia is fighting back. The Finnish company is switching to Microsoft's software from its own Symbian platform as part of an overhaul of its phone business set out in February.
But it recently abandoned hope of meeting key targets just weeks after setting them, raising questions over whether its new boss can deliver on the turnaround he promised.