Daniel Goodman / Business Insider
The service sounds similar to Venmo, which is now owned by PayPal.
The announcement is set to be made on Thursday at Google I/O, the company's annual conference for software developers.
Android Pay is a mobile payments API that lets 3rd party apps to process payments directly through their apps. It was reported in February that it would be separate from Google Wallet, Google's mobile payment product, but could be easily integrated with apps that use Google Wallet.
The Times report didn't provide any more details on how exactly the new peer-to-peer service would work, but it's a way for Google to attract more customers into its payments ecosystem, and gain more insights into the users' spending patterns.
It'll also give Google access to the mobile payments industry, which is expected to reach $142 billion by 2019, according to a Forrester Research report cited by the NYT.