Top test playing nations have shunned Pakistan since the 2009 attack on the visiting Sri Lankan players in Lahore with the PCB instead playing the majority of their home matches in the United Arab Emirates.
The PCB have managed to coax Zimbabwe into touring Pakistan this month for a brief limited over series which is currently underway but accept others are unlikely to follow.
"We would like to make India our home," Khan told the Hindustan Times newspaper.
"India will be more cost-effective," he said, adding Bangladesh and Sri Lanka have also offered to host home matches.
India cancelled bilateral cricket series with its neighbour after Pakistani militants killed 166 people in Mumbai in 2008 but hosted Pakistan in 2012-13 for a short limited over series.
Khan visited India earlier this month and said the neighbours are likely to play a full series in the United Arab Emirates in December.
While cricketing relations maybe thawing, political tensions still exist.
The duo have gone to war three times since their independence in 1947 and the prospect of Pakistan playing their home matches across the border is likely to meet with political opposition in India.
"We will cross that bridge when we come to it," Khan said.
(Reporting by Amlan Chakraborty in New Delhi; editing by Patrick Johnston)
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