If you cannot install non-standard software (example: customer owner, company operated RHEL boxes) you can get an idea of the current progress of cp/tar and similar programs by inspecting file-descriptor files in /proc.
Assuming that you have a process (like cp) with pid 1234, then in /proc/1234/fd you will find files with a number (corresponding to the file descriptor number in the context of the process) that are either symbolic links to the actual file or to socket connection (or other data structures). Let's assume that source file has fd 3 (you get this information via ls -l /proc/1234/fd )
Then, after you can cat /proc/1234/fdinfo/3 and look at the pos value: that's the position of the cursor in the file.
It's ugly and unpractical, but it should work on every Linux systems featuring basic tools.