Erica Joy, an employee of the search engine giant, said on her Google+ page: "For my iPhone using friends: the Google+ iPhone app has been submitted to the App store (no not today, sometime prior to today) and is awaiting approval".
However, Google has not confirmed it has submitted the app to Apple for approval.
It is hoped Google+, which was launched at the end of last month,will rival Facebook's popularity. The social network, which is currently in a 'limited field trial' and is only available to a select few, lets consumers share photos, chat to each other and leave messages and comments.
Furthermore, the social network benefits from Circles which lets users create lists of friends to share content with, as well as live video-chat for multiple users known as Hangouts, Huddle – a form of group instant messaging – and Sparks that lets users interact with others that have similar interests.
An app for handsets running Google Android that allows users to access the social network from their mobile phones is already available.
Apple has previously rejected apps for Google's Latitude and Voice services. In the case of Google Voice, Apple claimed the app offered the same function as one of the core features on the iPhone, subsequently breaking the app store's terms and conditions.