A notice calling for the meeting in parliament house makes no mention of the filmmaker, but BJP lawmaker Anurag Thakur, who heads the panel, told NDTV that both Mr Bhansali and Mr Joshi are expected to attend the meeting at 3 pm.
The notice for the meeting of the parliamentary committee on Information Technology says officials of the Information and Broadcasting Ministry will also brief panel members on challenges the department faces.
Among members of the parliamentary panel are Bollywood actors-turned-lawmakers Paresh Rawal of the BJP, and the Congress' Raj Babbar.
Earlier in the day, the censor board chief also appeared before the Lok Sabha Committee on Petitions to brief members about the controversy over "Padmavati" and said the film had not yet been approved and the board only cleared the trailer and promos of the period film, reported news agency PTI, citing sources.
Top union ministers have said Mr Bhansali should consult with opponents of the film and historians to arrive at a version that is acceptable to all.
The Chief Ministers of Rajasthan, Gujarat and Madhya Pradesh have said they will not allow the movie to release even if it is cleared by the censor board. On Tuesday, Bihar Chief Minister Nitish Kumar said "Padmavati" will not be screened in his state till Mr Bhansali clears the air on the objections raised against the film.
"Since objections against "Padmavati"are being raised from several quarters, its filmmaker should clarify his stand. As long as the controversy over the film does not subside, the film will not be released in Bihar," Mr Kumar said.
Sanjay Leela Bhansali has denied reports that his film suggests a romance between Rajput warrior queen Padmini and Delhi sultan Alauddin Khilji. Legend says the queen jumped into fire after her husband was killed in battle to ensure that Khilji would not capture her.
The Supreme Court on Tuesday turned down yet another appeal to ban "Padmavati" and reprimanded the Chief Ministers and others who have spoken out against the film, saying, "those holding public offices should not comment on such issues."
The judges said it is the prerogative of the national censor board to review the film and make a decision on whether it is suitable for screening.