Confirming the meeting Raj Singh Dungarpur of Cricket Club of India (CCI) said efforts were on to, "reach an understanding".
Both Bindra and Dungarpur were canvassing for Sharad Pawar for the president's post against Dalmiya's candidate Ranbir Singh Mahendra of Haryana.
Dungarpur said that they were opposing Mahendra's candidature because, "with Dalmiya as patron-in-chief the election of Mahendra as president would ensure that Dalmiya would be all over the BCCI".
Dalmiya, who completes his three year term today, has already been appointed patron-in-chief of the Board at a special general body meeting at Chennai on September 12.
At least 16 votes would be required to clinch a victory in the crucial election.
There are a total of 31 votes in the BCCI general body which include 27 state and other affiliates, three institutional affiliates - Services, Universities and Railways and one vote of the president.
The president, however, has a second casting vote in case of a tie in the voting.
The contest, however, does not entail normal election provisions like nominations and withdrawal as the names of the candidates can be proposed in the meeting itself and hence till the last minute there would be possibility of a consensus candidate getting elected without polling.
Following is the complete list of eligible voters:
North Zone: Jammu and Kashmir, Punjab, Haryana, Himachal Pradesh, Delhi, Services and Universities.
West Zone: Maharashtra, Mumbai, Cricket Club of India, Saurashtra, Gujarat and Baroda.
South Zone: Andhra Pradesh, Hyderabad, Karnataka, Tamil Nadu, Kerala and Goa.
Central Zone: Rajasthan, Uttar Pradesh, Madhya Pradesh, Vidharbha and Railways.
East Zone: Jharkhand, Tripura, Bengal, Orissa, Assam and National Cricket Club.