India are scheduled to play the Asia/Oceania Group 1 tie in the Pakistani capital on September 14 and 15.
But tensions between the neighbours have grown since India revoked the special autonomy status of Kashmir, which the nuclear-armed rivals have fought over since gaining independence in 1947.
Pakistan has frozen diplomatic ties and halted travel between the two countries. The All India Tennis Association said it has sought a meeting with the International Tennis Federation to force a change of venue.
"Mahesh Bhupathi, the Indian captain, has spoken to me. It is very concerning for the players to participate under such circumstances. They are looking for a remedy to play elsewhere," AITA secretary Hironmoy Chatterjee told AFP.
"We have told the ITF that the Indian ambassador has been sent back, diplomatic relations have been downgraded, airspace over Pakistan for Indian flights has been stopped, road and train connection is stalled.
The ITF said in a statement that it was satisfied with Pakistan's security plan for the event.
"We are working closely with the host nation and independent expert security advisors -- the ITF is satisfied with their current security assessment of the site and the security plan in place," the world body said.
"The overall security risk rating for Pakistan has not changed, however, we will continue to monitor the situation closely with our advisors."
On Monday, India's sports minister Kiren Rijiju said the government would not prevent the team from playing the Davis Cup tie in Pakistan as it was not a bilateral series and was organised by a world body.
India cut bilateral cricket ties with Pakistan after deadly attacks in Mumbai in 2008 that authorities blamed on Pakistani militants, with just one limited-overs tour in 2012-13.
An Indian tennis team last played a Davis Cup tie in Pakistan in 1964, when they beat the hosts 4-0. Pakistan lost 3-2 when they played in Mumbai in 2006.
Until recently, Pakistan has been forced to host Davis Cup ties at neutral venues as teams refused to travel to the South Asian nation over security concerns.