The speculations turned rife after a post shared by former Congress leader and BJP state spokesperson Narendra Saluja showed a picture of Kamal Nath with Nakul Nath captioned as 'Jai Shree Ram'.
Some videos of the incident surfaced on social media showing the fire with intermittent explosions taking place at the site and people running to save themselves.
AICC general secretary in-charge of Madhya Pradesh Jitendra Singh said the schedule of the yatra, including the date of arrival, will be announced later.
Suresh allegedly attacked his sister-in-law Nirmala with a rod and poured petrol on her before setting her ablaze, Superintendent of Police (SP) Rahul Kumar Lodha said.
Prime Minister Narendra Modi, Union Home Minister Amit Shah, Uttar Pradesh Chief Minister Yogi Adityanath, among others, are likely to attend the oath-taking ceremony at both places.
After the November 17 polls, the BJP retained power in MP by winning 163 seats in the 230-member assembly, leaving the Congress a distant second with 66 seats.
The source also said that the party was expecting 90 seats in Rajasthan as anti-incumbency was not there but there was anger against many of the sitting MLAs.
BJP appointed central observes to oversee meetings of legislative parties in Madhya Pradesh, Chhattisgarh and Rajasthan to elect their leaders who will be new CMs.