The BCCI insists the competition must either be staged in a neutral venue - like in 2018 - or their matches moved if the team are to defend their crown in September
Defending champions India will boycott the Asia Cup in September if the competition is hosted in Pakistan.
Political tensions between the two nations have grown in recent months in the wake of a Pakistan-based militant group taking responsibility for a suicide attack in Kashmir which killed 46 parliamentary police.
The 2018 tournament was moved from India to the United Arab Emirates due to difficulty in Pakistan's players obtaining visas.
If the seven-time winners are to take their place in this year's competition, which is to act as a warm-up for the T20 World Cup in Australia, then the BCCI want that move reciprocated.
"The question isn't about the PCB hosting the tournament," an official told news agency IANS.
"It is about the venue and as things stand now, it is quite clear that we would need a neutral venue.
"There is no way that an Indian team can visit Pakistan to even participate in a multi-nation event like the Asia Cup.
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"If the Asian Cricket Council (ACC) is ok with an Asia Cup minus India then it is a different ball game.
"But if India is to participate in the Asia Cup, then the venue cannot be Pakistan."
After the PCB rowed back on suggestions they would themselves pull out of the T20 World Cup in India in 2021, chief executive Wasim Khan has opened the door to India's matches being played away from Pakistan.
"Since we have been awarded hosting rights, we fully expect the Asia Cup to happen in Pakistan," he said.
"The ACC will then need to make a decision as to where they will play the India games."
Following the 10-year anniversary of the Lahore shootings, major cricket events are slowly making their back to Pakistan. A Test series against Sri Lanka was hosted last year, while Bangladesh are currently in the middle of a multi-format tour.
And in February and March, the Pakistan Super League will be played entirely on home soil for the first time.
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