The tech giant recently confirmed the smartphone's security system can allow access to a person's device even in the event their eyes are shut.
In a statement, the company said: "Pixel 4 Face Unlock meets the security requirements as a strong biometric."
However, they have admitted they want to change it so the eyes are required to be open to keep their device secure.
According to The Verge, the firm said that they have "been working on an option for users to require their eyes to be open to unlock the phone, which will be delivered in a software update in the coming months."
As a comparison, Apple's Face ID system makes sure the user is "alert" and facing the phone before it can be unlocked.
Before the model was launched, Pixel product manager Sherry Lin insisted: "There are actually only two face [authorisation] solutions that meet the bar for being super-secure. So, you know, for payments, that level - it's ours and Apple's."
BBC News tested the device using default settings, with the same result happening when several people pretended to be asleep.
Before the Pixel 4 was released, leaked images showed a setting in the facial recognition menu which said: "Require eyes to be open."
However, the setting wasn't present on the devices used by the publication, and Google confirmed the option won't be included when the product goes on sale on October 24.
On Google's Pixel 4 support website, the company tells customers: "Your phone can also be unlocked by someone else if it's held up to your face, even if your eyes are closed."
While the company told BBC News that Face Unlock can't be tricked by masks or photos, it added: "We will continue to improve Face Unlock over time."