The long-running saga over the Google Voice iPhone app looks set to be nearing an end, with unconfirmed reports suggesting that Apple has finally agreed to accept the VoIP app on the App Store.

According to US website TechCrunch, official confirmation by Apple is due in a matter of weeks; sources say that the app has already been approved pending some technical adjustments that need to be made by Google for the final version. Some third-party apps that allow access to Google Voice have already appeared on the App Store in recent weeks in a further sign that Apple is softening its stance.

Apple’s decision last year to block all Google Voice apps sparked major controversy in the US, and was subsequently the subject of an investigation by the FCC, the US regulator. Apple said that it banned the apps because they “duplicate” the iPhone’s core mobile functionality for voice calls, text messaging and voicemail. However, critics argued that Apple may have colluded with AT&T – the exclusive iPhone operator in the US – to block a service that threatened to cannibalise the operator’s voice revenue. In its letter to Apple, the FCC asked for the reason behind the rejection and the decision to remove the third-party apps. It also asked whether Apple acted alone or in consultation with AT&T, and what role AT&T had played in the approval process.

Apple’s decision to now allow such apps is being linked to the overhaul of its App Store guidelines, which were published earlier this month and provide developers with a more transparent view of what kind of apps will be barred from the store. TechCrunch notes that “none of the rules seemed to apply to Google Voice.”

Not much is known about the official Google Voice app, though the report notes that it is likely to include features not currently available on third-party apps such as push notifications for inbound SMS and voicemail messages (as Google does not provide an API for these).