There is no need of Linked Server to configure Mirroring between two databases on different instances.

You just need to check these points:

There is connectivity between both the instances.

Both the instances are using same version of SQL Server(like you can configure Mirroring between SQL Server 2008 and 2012, however it will only work if 2008 is primary and till first failure. As soon as 2012 becomes Primary after first failure, the mirroring will break and cannot be configured.)