Advani, who was deputy Prime Minister in the previous NDA government, with his vast experience and stature was reportedly not keen on a role in a government headed by Modi, once considered his protege.
There were talks of Advani being offered the post of NDA parliamentary party leader or Speaker of the next Lok Sabha.
The party will also have to decide on the part to be played by another veteran Murli Manohar Joshi, a former BJP president, who was reportedly unhappy when he was shifted from Varanasi to Kanpur to pave the way for Modi to contest the seat.
Though Singh remained tightlipped about the agenda of their meeting with Modi, issues like formation of the next government and tasks to be assigned to seniors like Advani, Joshi and Leader of Opposition in the Lok Sabha Sushma Swaraj were possibly discussed.