No. Only U.S. citizens are eligible to sponsor a fiancé(e) for a K-1 visa. Permanent residents (green card holders) do not have the option to bring a fiancé(e) to the U.S. through this process.

As a permanent resident, your available route is to marry abroad and file a spousal petition (Form I-130). This process may take longer than a K-1, but it is the only option until you naturalize.