Ganguly was accompanied by coach John Wright, Jagmohan Dalmiya and lawyers Siddhartha Shankar Ray and Ushanath Banerjee.
The teleconference began at the scheduled time but got delinked for some time before it started again.
Match Referee Clive Lloyd, who reported Ganguly to ICC, is scheduled to join the conference call from USA.
ICC's in-house lawyer Urvasi Naidoo is also involved in the call in an administrative capacity.
Ganguly was slapped a two-Test ban by the ICC for slow over rate in the Platinum Jubliee one-day match against Pakistan in Kolkata on November 13. After the skipper appealed against the ban, the ICC appointed New Zealand legal expert Castle to decide on the appeal.
The ICC had said yesterday that it has requested the Appeals Commissioner to take a decision on Ganguly's appeal before the second Test between India and South Africa beginning in Kolkata on Sunday.
After the teleconference, Castle will consider the evidence he has heard from all the parties along with the grounds of the appeal, match paperwork from Lloyd and video of the match.
Castle will then provide a written decision to the ICC which will then be forwarded to Ganguly, Lloyd and ICC Chief Executive Malcolm Speed.