Here are the 10 latest developments in this big story:
The PM met with the BJP's parliamentary board, its top decision-making body. Present at the session was Foreign Minister Sushma Swaraj, who has refuted reports of being a top contender for President.
The opposition has said its preference is to be formally informed of the BJP's choice before deciding whether it will field its own candidate.
Bihar Chief Minister Nitish Kumar said today that so far, no candidate has been shared for discussion by the government. Time is running out, the opposition leader warned. "They haven't decided on any name until now..we can wait for 2-3 days but we cannot wait forever."
BJP chief Amit Shah made an important visit yesterday - to disgruntled ally Shiv Sena to seek its support. Sena chief Uddhav Thackeray is keen on either MS Swaminathan, scientist and father of India's Green Revolution or Mohan Bhagwat, who is the chief of the BJP's ideological parent, the Rashtriya Swayamsewak Sangh or RSS.
If an election is held, the BJP and its allies are positioned to make their candidate win because regional parties, including some from the south, have promised to back the ruling alliance.
The BJP has assigned three senior ministers - Rajnath Singh, Arun Jaitley, Venkaiah Naidu - to consult with allies like the Sena and opposition parties.
On Friday, the BJP's representatives met with Congress chief Sonia Gandhi and Mr Yechury of the CPM.
In the two last Presidential elections, the Sena supported Pranab Mukherjee and Pratibha Patil, both of whom were candidates of the previous Congress-led government. So the Sena voted in favour of the BJP's rival.
All BJP lawmakers and ministers have been summoned to Delhi as the party gears up for the nomination process of its candidates.
Prime Minister Narendra Modi departs for the US on Friday so all formalities are likely to be completed before then.
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