Among those who have offered to resign are Union Minister Kalraj Mishra, Uma Bharti, and Minister of State for Human Resource Development Mahendra Nath Pandey, who was appointed Uttar Pradesh State BJP chief.
The restructuring is expected to take place by Sunday before Prime Minister Narendra Modi leaves for a BRICS convention.
Rudy and Bharati are likely to be given organisational roles in the party, ahead of the 2019 general poll, BJP sources said.
Sources said Rudy has resigned from the post of Minister of State (Independent Charge) of the Skill Development Ministry.
Janata Dal (United), which recently joined the ruling National Democratic Alliance, is likely to get a berth in the new Cabinet. The meeting was attended by Finance Minister Jaitley. By appointing Pandey as the UP BJP chief, the party has made sure the Brahmin community will not be upset with Mishra's removal.
In his first comments after being asked to resign as minister, Rajiv Pratap Rudy told NDTV that "It's not my decision, it's the decision of the party, and I will follow (it)".
Sources in the BJP said that a reshuffle may take place either on Saturday or sometime after the Prime Minister's return from China and Myanmar. She has been keeping indifferent health for the past few months and reportedly wants to work for the Namami Gange project as well as work for the BJP.
Venkaiah Naidu also resigned from the Information and Broadcasting ministry and the central government as he became the President of India.
With the exit of Manohar Parrikar and M Venkaiah Naidu from the Government and the passing away of Environment Minister Anil Madhav Dave, the Council of Ministers is now being left with three vacant positions.
Speculations are going on that Minister for Road Transport and Highways and Shipping, Nitin Gadkari, might get an additional charge of Railway ministry after Suresh Prabhu offered to resign from his post following multiple train accidents in recent times. Karnataka would have assembly polls next year. Junior Health Minister Faggan Singh Kulaste were also learnt to have been summoned by the BJP president.