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On the basis of the world rankings, India, who were seeded No.1 in the Asia Pacific draw, will be overwhelming favourites to win and advance to the World Group qualifying round.
The problem is that the Indian government froze all sporting ties between the countries after the deadly attacks on Mumbai in 2008 which were blamed on Pakistan-based militants.
"AITA does not have a choice," the All India Tennis Association Secretary General Hironmoy Chatterjee told Indian news agency PTI.
"We have to follow the government policy. We will speak to the government to know. They have not allowed any sports team to travel to Pakistan."
The tie is due to be played in September.
There is a long history of sporting boycotts between the countries and no foreign cricket team has toured Pakistan since Pakistan hosted Uzbekistan and South Korea last year on grass courts in Islamabad.
India and Pakistan have met six times in the competition, though three of those meetings came in consecutive seasons from 1962-4. India have won every time, racking up an emphatic 23-4 aggregate score in total rubbers.
In 1971, the two nations were drawn together but the tie was not played with India awarded a walkover.
India have played in Pakistan twice, both times in Lahore, but the most recent of those visits was in March 1964, with India winning 4-0.
The two nations met at a neutral venue, in Kuala Lumpur, in 1972.
Pakistan have visited India since, losing at the Brabourne Stadium in Mumbai, 3-2, in 2006. That was the only time Pakistan have taken India to the final rubber.
"It's a good draw for us with the depth in our team," said Mahesh Bhupathi, who played in the winning doubles pair in 2006 and is now India's Davis Cup captain. "We are looking forward to winning and getting back to the World Group Play-offs again."
Neither Bhupathi nor India coach Zeeshan Ali would comment when asked by PTI if the government should allow the team to travel, or if they are willing to travel, to Pakistan.
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