The tie was earlier scheduled to be held in Islamabad on September 14-15 but was postponed to November after an in-depth security review by the International Tennis Federation last month.
An Indian tennis team last played a Davis Cup tie in Pakistan in 1964, when they beat the hosts 4-0.
The all-important meeting, which was postponed to Tuesday from Monday, has now been called off.
The meeting which was initially supposed to take place on Monday will now take place on Tuesday.
The ITF has shared their security plans with AITA and offered them to have a discussion on Monday with their security consultants.
Surprised with the fact that AITA has sought just a security re-check from the International Tennis Federation, Mahesh Bhupathi said, "We have asked AITA to request for a neutral venue".
The tie is scheduled for September 14 and 15 in the Pakistani capital and the federation had begun the process to procure visas for the players.
Prajnesh Gunneswaran and Ramkumar Ramanathan will lead the singles challenge while Rohan Bopanna and Divij Sharan will make the doubles pair for the grass court tie.
The Indian tennis players are "excited and available" to travel to Pakistan for the upcoming Davis Cup tie but want to be assured that all the security measures are in place.
No Indian Davis Cup squad has travelled to Pakistan since March 1964 and in that tie, held in Lahore, India had won 4-0.
India's sporting stars praised the Indian Air Force after the air-strike across the Line of Control.
Boris Becker urged Leander Paes, Mahesh Bhupathi and Sania Mirza to team up to take the game forward in India.
No Indian Davis Cup squad have travelled to Pakistan since March 1964.
Andreas Seppi guided Italy into the first finals of the revamped Davis Cup after beating India 3-1 in the world group qualifier.
Italy took a 2-0 lead in the second rubber of the Davis Cup World Group qualifier tie.
The venue boasts of an impressive 8-2 win-loss record for India, including the solitary victory over Italy in the 1985's World Group 1st Round.
Leander Paes has been left out of the squad on basis of his world ranking.