Rajnath, a former chief minister of Uttar Pradesh, is one of the tallest leaders of the party from the heartland state and many in the BJP believe that only an "experienced and capable" leader like him can run the most populous state that sends 80 MPs to the Lok Sabha.
Rajnath appeared to scoff at the speculation. Asked if he could become chief minister, he said such talk was "unnecessary and futile speculation".
Sources close to Rajnath, however, indicated that the leader might not be averse to the idea provided he was offered the job by Narendra Modi and Amit Shah.
The sources said Rajnath felt that being the chief minister of a big state like Uttar Pradesh was any day better than being a minister in the Modi government. "As Uttar Pradesh chief minister, he will be the boss. Here, he is working under the big boss," a BJP leader said.
Many in the BJP discounted the possibility of Rajnath being made chief minister as the Modi-Shah combine would not prefer to appoint someone who could defy their authority.