How can I upgrade to core 9? I have Drupal 8.8.* and I would like to migrate to Drupal 9 using Drush 8. I know, we can use composer however I just wanted to confirm, whether we can do by using Drush command? 

I tried using Drush but it's showing no updates available. 

$ drush pm-update drupal-9.0.0
Update information last refreshed: Thu, 06/11/2020 - 11:42
 Name    Installed Version  Proposed version  Message                     
 Drupal  8.9.0              8.9.0             Specified version not found 


No code updates available.
No, you can't. drush pm-update has been deprecated for a while. The command is still available in the Drush 8.x branch but in later revisions it only exists as a signpost to inform the user how to move to Composer:


  The pm-updatecode command was removed. Please see composer update --dry-run and composer update.


Noting that Drush 8 isn't supporting revisions past 8.3.x or 9.x, you should look into upgrading Drush and moving to a Composer-driven upgrade process.