There is and there never was a native Picasa for Linux version.
What Google always did was to wrap Picasa in a nice package containing Picasa and a custom version of Wine.
If you want to install Picasa in Linux it always has to use Wine, either installed by you or using the packages from Google that contain Wine. In the end its your choice and will lead to the same.
Because the Linux installation is just a Wine wrapper with the Windows binaries, Google has discontinued the support for Linux and the last available package in their repositories is for Ubuntu 11.10, version 3.0.
Google explains that if a Linux user needs to use Picasa he can use the Wine version installed in Ubuntu to run the Windows binaries, making no sense to invest time developing something extra.
Google wrong on their blog on April 20, 2012:
"(...)today, we’re deprecating Picasa for Linux and will not be maintaining it moving forward.” (source)
They also explain that maintaining the package for Linux is becoming harder since and that is costing them time compared with Windows releases.
For instruction on how to install Picasa 3.9 in your system please have a look at