The meeting of the board will be held a day before the end of nominations for the vice-presidential elections.
The meeting will be attended by Prime Minister Narendra Modi, party chief Amit Shah and other members of the board.
Congress and several other major opposition parties have already declared former West Bengal Governor Gopalkrishna Gandhi as their vice-presidential candidate.
Polling in the vice-presidential election will be held in August 5 and counting will take place the same day.
Meanwhile, Prime Minister Narendra Modi on Sunday thanked all political parties for a very dignified campaign for the July 17 presidential election.
"It would have been better if there was a consensus for the President's election. But, the election campaign for this election was very dignified. There was no instance of use of harsh words or feelings. I thank everyone for this," Modi was quoted by a Union Minister as saying at an all-party meeting in Parliament House Complex here, ahead of Parliament's monsoon session from Monday.
Parliamentary Affairs Minister H.N. Ananth Kumar said Modi later appealed to all the members of parliament and state assemblies to vote in the President's election.
He thanked all political parties for their support in the passage of the Goods and Services Tax (GST) Bill and related legislations and sought their assistance for the smooth implementation of the legislation.
Modi said the programme for the celebration of the 75th anniversary of Quit India movement -- launched by Mahatma Gandhi on August 8, 1942, to demand an end to British rule in India -- will be discussed in both houses by the government.
The Prime Minister expressed concern over the flood situation in north-eastern states, and said "the government is taking all steps to provide help".
Those who attended the all-party meeting included Ghulam Nabi Azad and Jyotiraditya Scindia from the Congress, Sitaram Yechury of the Communist Party of India-Marxist, D. Raja of the CPI, Sharad Pawar and Tariq Anwar from the Nationalist Congress Party, H.D. Deve Gowda from Janata Dal-Secular, Farooq Abdullah from National Conference, Mulayam Singh Yadav from Samajwadi Party, Jaiprakash Yadav of the Rashtriya Janata Dal, M. Rajamohan Reddy from YSR Congress Party and A.P. Jithender Reddy from TRS.
Trinamool Congress boycotted the meeting while no representative of Nitish Kumar's Janata Dal-United was seen.