Is it possible to get access to files uploaded via FTP in the media module in Drupal 7
Is it possible to get access and select FTP uploaded files via media module?


No.

When you upload the files yourself (via FTP or some other means that is not part of Drupal), they will not be recognised or known by the Media module.

There are a helper module called Filefield Sources that let you add files downloaded with FTP to Drupal media management modules.  A variation called IMCE Filefield currently integrates with the IMCE module, but there is AFAIK nothing similar for the Media module. 

It has suggested to integrate Filefield Sources with the Media module. However, there does not seem to be anybody working on it, (just a lot of people who want it).

If you really want this, you probably need to add this to the Filefield Sources yourself.