The Brazilian forward suffered a medial collateral ligament injury during City's game against Crystal Palace before the start of the new year and is expected to be sidelined until February.
After a protracted transfer saga which began in the summer, Van Dijk eventually moved to Anfield earlier this month for a huge fee, becoming the world's most expensive defender in the process.
Crickerters could be taken off the field in extreme heat to avoid a repeat of the day which saw England captain Joe Root hospitalised with dehydration during the fifth Ashes Test.
The Spain international has featured three times since becoming eligible to play for Atletico. He joined the club from Chelsea in September but could only be registered at the start of the month.
The Santiago Bernabeu club won La Liga and the Champions League last season but they have been less successful this time out - they already trail leaders Barcelona by 16 points.