Y.S. Chowdary, C.M. Ramesh, T.G. Venkatesh and G. Mohan Rao called on Shah and expressed their willingness to join the BJP. They are likely to send a letter to the Rajya Sabha Chairman, informing them of their decision.
The development may plunge the TDP into a crisis at a time when party President and former Andhra Pradesh Chief Minister N. Chandrababu Naidu is on a foreign trip along with family members.
Chowdary, a former central Minister, and Ramesh are considered close to Chandrababu Naidu. The two MPs had faced series of searches by Income Tax, Central Bureau of Investigation (CBI) and Enforcement Directorate (ED) in recent months.
In another development, some TDP leaders including former legislators held a secret meeting at Kakinada amid reports that they are planning to join either BJP or YSR Congress Party (YSRCP).
Under the leadership of former MLA Thota Trimurthulu, TDP leaders belonging to Kapu community held a meeting a hotel at Kakinada on Thursday to discuss their strategy.
The developments came amid claims by BJP leaders that several leaders from various parties in both Andhra Pradesh and Telangana were keen to join their party.
The TDP lost power to YSRCP in Andhra Pradesh in the recent elections. The party could secure only 23 seats of the 151 Assembly seats. It won only three of the 25 Lok Sabha seats in the state.