The Wall Street Journal says that a test version of the Google Maps app has been given to some individuals within the company. It cites "a person with direct knowledge of the matter" as its source.
However, the Journal notes that it is "unclear exactly when that will happen". The paper also did not indicate whether the app would be optimised for iPads.
There is also the question over whether Apple would approve the Google Maps app, as it would compete with its own Maps service that is pre-installed on iPads, iPhones and iPod Touch devices.
An Apple spokesman declined to comment on the report.
A Google spokesman did not confirm the plans but instead said: "We believe Google Maps are the most comprehensive, accurate and easy-to-use maps in the world.
"Our goal is to make Google Maps available to everyone who wants to use it, regardless of device, browser, or operating system."
Apple and Google are locked in a battle for the digital maps market, which is considered a key growth area as people increasingly find places to visit, shop and eat on their mobile devices.
In mid-September, Apple released the iOS 6 mobile operating system that replaced the previous Google Maps app with Apple Maps as the pre-installed service.
However, the move backfired as Apple's own maps system was hit with widespread criticism, prompting a public apology from Apple chief executive Tim Cook.
Apple's iPhone software boss Scott Forstall refused to apologise publicly for the embarrassment, contributing to Cook's decision to force him out of the company last month.
Maps has now been brought under the responsibility of Apple's executive for software and services Eddy Cue, who is overseeing renewed efforts to fix the bugs and improve the service.
However, Google is now expected to move in with its own iOS maps app, offering turn-by-turn navigation.
While the maps debacle has boosted the profile of Android, the chance to reach Apple's massive iDevice user base with Google Maps is likely to prove more alluring for the search giant.