There's an easy and a complex answer to your question. The easy one is no, with plain ASP you're note getting anywhere. However, using (J)TAPI (and it only works using those two technologies), you can track ongoing calls. Now if you could find a COM wrapper for Cisco's TAPI, you might be able to use it in ASP (but I only know JTAPI so I'm not sure if there would be any limitations doing the whole thing with TAPI). The probably more straightforward solution is to use JSP (Java based) and JTAPI. There's a good example for that, an example that upon call presentation on the phone, looks up the caller number in the LDAP directory and sends an XML page to the phone for display.
This example is called Callerinfoserver and you'll find it in the IP phone services SDK which you can download from this url: http://www.cisco.com/cgi-bin/dev_support/access_level/product_support