Parmar had to take charge during the fourth Test after lead physio Nitin Patel was forced to self-isolate after being identified as a close contact of Shastri.
Ahead of the fifth and final Test against England, Parmar tested positive for COVID-19 in Manchester. This had led to Team India's training session for Thursday afternoon being cancelled.
An ECB spokesman said later Thursday that all subsequent PCR tests from within the India squad had produced negative results and that the Test match "goes ahead".
However, there are no COVID-19 related worries in the England camp and Jos Buttler said everything is fine and the hosts are looking forwrd to the game.
"We don't know too much about it at the moment. It would be naive to speculate on what's going on. At the moment we're fully expecting the game to go ahead and we're preparing that way so fingers crossed the game will go ahead. Things are fine in our camp and we are looking forward to the game," said Buttler in a virtual press conference.
This came after India head coach Ravi Shastri, bowling coach Bharat Arun and fielding coach R Sridhar returned positive results to their RT-PCR tests during the fourth Test.