Mr Whittaker has launched an online survey on his website asking people to vote for their preferred candidate.
He said: "Who do you think it should be? With the leadership of our country at stake following the Prime Minister's decision to stand down, I would really appreciate your views, to get a grasp on how my constituents feel."
He has also posted on social media: "Let me know via our survey and I will take your views into consideration."
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The first stage of the procedure to choose a new Prime Minister started today, with Conservative MPs voting this afternoon and a result expected at around 5pm.
To proceed to the next ballot of MPs, candidates need to secure at least 30 votes in this round.
There will be more MP votes, with the candidate with the fewest votes eliminated each time, until only two remain.
Members of the Conservative Party will then be asked to make a postal vote, with the winner of that declared Prime Minister.
To share you views, visit https://www.calderdaleconservatives.uk/news/craig-whittaker-mp-launches-next-prime-minister-survey