The rest of the suspended IPL is unlikely to be played in India with the BCCI also unclear whether a window can be found to play the 31 games that are left.
The IPL had been suspended indefinitely last week after many tested positive for COVID-19 within the bio-secure bubble in Ahmedabad and New Delhi.
Sourav Ganguly, head of the Board of Control for Cricket in India (BCCI), told Sportstar magazine that COVID-19 restrictions meant it was impossible to stage the remaining games in India.
"There are lots of organisational hazards like 14-day quarantine. It can't happen in India," Ganguly said.
"This quarantine is tough to handle. Too early to say how we can find a slot to complete the IPL."
Warwickshire, Surrey and the Marylebone Cricket Club (MCC) are keen to host the remaining matches in September, but a BCCI official told Reuters on Friday they were yet to discuss the offer.
The entire 2020 tournament was played in the United Arab Emirates because of the pandemic.
Ganguly also said India would play three one-dayers and five Twenty20 Internationals in Sri Lanka in July though the BCCI is likely to field a second-string squad.
The Virat Kohli-led India side are set to leave for England in early June for the World Test Championship final in Southampton against New Zealand. They will then play a five-test series against England.
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