DSL(Digital Subscriber line) Will become Ethernet(or usb in some cases) by the time it hits your pc, so by then the phone system is no longer a part of it.
This is because DSL operates on a different frequency from the phone lines and Caller ID will not pass through the modem as far as I know.
If you have a regular FAX modem in the PC, there may be some software to do that.
Google shows this, never tried it(and it is very old), there may be other software. This only works if you have the modem connected to the phone line.