Union Government
(1) No person shall be eligible for election as President unless he - (a) is a citizen of India, (b) has completed the age of thirty-five years, and (c) is qualified for election as a member of the House of the People. (2) A person shall not be eligible for election as President if he holds any office of profit under the Government of India or the Government of any State or under any local or other authority subject to the control of any of the said Governments.
To become President, a person must be an Indian citizen, at least 35 years old, and eligible to be a Lok Sabha member, and must not currently hold any other government "office of profit" (a paid government position) - being President, Vice-President, a Governor, or a Minister doesn't count against this rule.
A sitting Chief Minister or Cabinet Minister who wishes to contest for President would need to consider these eligibility rules, though the Constitution specifically exempts holding certain constitutional offices (like being a Minister) from counting as a disqualifying "office of profit".