In a statement on its website, the company said its iPhone application "should be available in a few weeks."
"The demo (application) is currently under evaluation ... so there is no specific launch date for it yet," Spotify's Annina Svensson told AFP.
"We are very confident. We have top level contacts at Apple directly and we are still talking to them," she added.
If Spotify does become available on the iPhone, users will be able to save up to 3,000 songs to their handsets.
Music fans would then be able to listen to their favourite tunes even in areas with poor mobile internet reception.
"It would be fantastic for our users to have a real on-demand service on the iPhone that is easy to use, economic and very fast," Svensson said.
The service, which first launched last year, is seen as a potential rival to iTunes because of its huge, free library of millions of songs.
Spotify is currently only available in Sweden, Norway, Finland, Britain, France and Spain.
Music fans can sign up for the company's ad-supported free service or a premium service with no commercials that costs €9.99 euros a month.
Svensson said the planned iPhone application would only be available to Spotify's premium customers if approved.