The Board of Control for Cricket in India (BCCI) opposes a recommendation that would prevent cricket from being played up to 15 days after the cash-rich Indian Premier League (IPL) finishes.
The eight-team Champions Trophy begins on June 1, likely to be just days after the glitzy IPL final which is usually held in the last week of May.
The 15-day window has been proposed to avoid player burnout, but the BCCI says the break will result in huge financial losses and difficulties in rescheduling a packed cricket calendar.
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"I don't know whether India will be able to play Champions Trophy in England next year or not," Thakur told reporters in Kolkata during the second Test against New Zealand.
"As per the recommendations you have to give a 15-day window before and after IPL. There is Australia series before IPL and Champions Trophy after it.
"So BCCI has to make a call whether they will play IPL or Champions Trophy."
India's Supreme Court has ordered the BCCI to implement sweeping organisational reforms proposed by a panel headed by former chief justice Rajendra Mal Lodha.
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The BCCI -- one of the most powerful bodies in world sport -- rejected some of the reforms, including the 15-day window, at a special general meeting in Mumbai last week.
The Supreme Court has accused the BCCI of "behaving like lords" and told them to "fall in line".
Thakur insisted reforms were being made after the IPL was dogged by match-fixing and corruption scandals, but warned of the financial impact. He said the BCCI would file a report to the Supreme Court for its next hearing due on October 6.
The chief also dismissed any chance of a first bilateral series with Pakistan since 2012 and said the body was open to the use of the much-debated Decision Review System (DRS) in the future.
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"Forget about playing Pakistan, first let's see whether we are able to play Champions Trophy or not. The chance of playing Pakistan only arises if we participate in Champions Trophy," said Thakur.
DRS, which includes the Hawk-Eye ball-tracking technology, is optional for Test matches and only used if both sides agree to it.
India is the only side that refuses to use the technology, designed to help umpires make the right call. Thakur said only when the system can be proved to be "100 per cent" fool proof would the BCCI reassess its stance.
"If that is satisfactory then BCCI is open to use DRS," he explained.
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