Until they add this, I'm afraid you'll have to search and ask for each asset. It's unfortunate that the Asset Store page does not provide a clear 'license' section. To start, let’s download a free 3d character model off of the Unity Asset Store. I'm not exactly sure what license apply here, so I'll suggest you ask the author what are the terms of use of their asset before you commit to it. Find this & more VFX Shaders on the Unity Asset Store. If you get the SciFi Robots, you'll find no license on the Asset Store page, and no readme and no license.txt in the package. The Vegetation Engine Free Shaders for Creators VFX Shaders Unity Asset Store Add depth to your next project with The Vegetation Engine Free Shaders for Creators from BOXOPHOBIC. If you get the Standard Assets provided by unity, you'll have to dig, find, read and understand the actual license, where there is no mention that you must credit the author Check out the wildly popular free assets, and grab them for your next project. If you get the 'Unity-Chan!' Model, you'll have to display somewhere the 'license logo or the license sign separately' as specified by the “Unity-Chan” License Terms and Conditions

I'm assuming that by 'free asset', you mean an asset available on the unity Asset Store that is shown when filtering by 'free' ( resulting in something like this).

Unity assets store free