Rudy is expected to be given an organisational assignment in the BJP, sources close to him said.
Sources said Kalraj Mishra, who had met Shah on Thursday, might also resign. He is well above 75 years, the age bar the party has informally set for ministers.
Earlier in the day, Union minister Mahendra Nath Pandey was appointed Uttar Pradesh BJP president in place of Deputy Chief Minister Keshav Prasad Maurya, creating one more vacancy in the Council of Ministers.
The reshuffle might take place before Modi departs for China to attend the BRICS summit.
Water Resources Minister Uma Bharti has also reportedly offered to quit on health grounds.
AIADMK's Thambi Durai and K Venugopal are being seen as among likely representatives of their party in the Cabinet if the Tamil Nadu party joins the Modi government. At least two members of the JD(U) are also likely to join.
There are several vacancies in the government while some senior ministers, including Arun Jaitley and Harsh Vardhan, are holding additional portfolios.
The President is scheduled to leave for Tirupati on Friday. As of now, nothing has been communicated to the Rashtrapati Bhawan, according to sources.