The Telangana issue, a decision on which was deferred last week by the Centre, is believed to have come up for discussion at length during the meeting between Reddy and Singh.
Reddy also met Shinde separately and discussed the issue, which has divided the state on regional lines.
The chief minister had on Monday held consultations with Congress president Sonia Gandhi, her political secretary Ahmed Patel and party general secretary Ghulam Nabi Azad on the Telangana issue.
The meetings come in the wake of Congress' announcement that it was not opposed to creation of a separate Telangana state.
Party spokesman PC Chacko had last week said discussions were on at various levels on this issue.