The meeting has been facilitated by the Bengal governing body IFA secretary Utpal Ganguli.
"Before taking a decision (on running both I-League and ISL simultaneously) I requested the AIFF president to meet us," Ganguli said.
"He has given us time on Saturday and there will be both the clubs and myself. We hope to put forward our case," he added.
It has been learnt from the AIFF executive committee meeting in Mumbai today that Patel want to run both the leagues for the 2017-18 season as a solution to the prevailing deadlock in Mohun Bagan and East Bengal's induction into ISL and giving it the official top-tier status.