Both captain Amritraj and coach Zeeshan Ali's contracts are up for review and the speculation is that AITA may not renew Amritraj's contract since it had been reported recently that he had failed to ensure discipline in the team.
AITA officials have said that there may be a change as they would like to see rules and disciplines be implemented.
Terms of both Amritraj, who had replaced SP Misra and Zeeshan, who came in place of Nandan Bal, will end later this month and India's next tie is against New Zealand in Pune from February 3-5.
India's top four singles players, including Somdev Devvarman, Yuki Bhambri, Saketh Myneni and Ramkumar Ramanathan have requested AITA to retain both Amritraj and Zeeshan since the team has produced good results under them.
"We are writing this letter to express our total support for Anand Amritraj as Captain and Zeeshan Ali as Coach of the Indian Davis Cup Team. It has come to our attention through media that there are rumours of a possible change, and we are all strongly opposed to any such change," the letter sent by the players in October stated.
"We would like to request the AITA to retain Anand as Captain and Zeeshan as Coach of the Indian Team for the foreseeable future. They have done a great job of bringing peace and harmony to the team, especially in difficult away matches.
"We have done quite well to reach the World Group Playoffs all 3 years that Anand and Zeeshan have been there, not to mention good showings against Serbia and the Czech Republic in 2014 and 2015. We would like the AITA to respect our wishes in this matter and leave the team unchanged," the letter stated further.
It was on the players insistence that in 2013 the then captain S P Misra and Nandan Bal were removed and replaced by Amritraj and Zeeshan.
However, AITA Vice President Bharat Oza had said recently in Pune that it is AITA's "prerogative to decide on the issue" and they actually did not appreciate a few comments made by the players at that time.
The names of former Davis Cupper and captain Ramesh Krishnan and Bal are doing the rounds as possible replacement of Amritraj.
The AITA also did not appreciate the fact that Amritraj had criticised the evening timing for the Davis Cup tie against Spain. Amritraj had later gone on to say that in hindsight, he changed his mind.