"We have received advice from a variety of sources referring to traveling to India,'' Tennis Australia chief executive Steve Wood said in a statement Thursday. "It is on that basis of security concerns that we have asked for the tie to be moved out of India.
"The ITF has received our request and is doing its own security assessment. The safety of our players and staff is of paramount importance to Tennis Australia.''
The winner of the Asia-Oceania Group 1 match, scheduled for May 8-10, will advance to the playoffs for a spot in the elite world group.
In London, the International Tennis Federation confirmed it had received Tennis Australia's request to switch venues, and had asked its security advisers to submit a report which it hopes to receive next week.
The ITF said there would be no discussion of alternative venues until it had reviewed that report and, until then, the match would take place in Chennai as planned.
The All India Tennis Association said in a statement that it was confident of the match being held in Chennai.
"There's no need to shift it,'' the statement said. "The International Tennis Federation wrote to us about Australia's security concerns and we've sent a reply.''
The Indian Premier League Twenty20 cricket tournament was moved this week to South Africa due to security concerns in India.
A terror attack on the Sri Lanka team in Lahore, Pakistan earlier this month heightened concerns about security for sports events on the Indian sub continent. Seven test players, an assistant coach and a match official were among those injured. Six policemen and a driver were killed in the ambush by heavily armed gunmen.
In November, terror attacks in India's financial capital Mumbai left 164 people dead and forced the cancellation of a Champions League Twenty20 cricket tournament involving provincial teams from five countries.