The parliamentary board of the BJP, its top decision making body, will be meeting in the national capital Wednesday.
Shah, who has been credited with the party's impressive performance in Uttar Pradesh, will be stepping in the shoes of party leaders like Atal Bihari Vajpayee, L.K. Advani, and Murli Manohar Joshi.
Shah -- if picked for the post -- will succeed Rajnath Singh, now the home minister in the Modi government.
Shah played a key role in the Bharatiya Janata Party's landslide victory in the Lok Sabha election in Uttar Pradesh where it won 71 of the 80 seats.
Known to be a sharp political strategist, the former Gujarat home minister remains Modi's most trusted political aide and masterstrategist.
Shah, who had a plastics and printing business, met Modi in the late 1980s.
It was earlier said that Shah, who is currently BJP's national general secretary, may contest from Vadodara Lok Sabha seat that was vacated by Prime Minister Narendra Modi who retained Varanasi constituency.