CSK defeated KKR by six wickets in the Indian Premier League (IPL) here on Thursday.
Kuldeep has spent the last two matches warming the bench, with the uncapped Varun Chakravarthy preferred over the India spinner.
The Chinaman bowler got just four wickets from nine matches in 2019 and was dropped from KKR after logging an average of 71.50 and an economy rate of 8.66.
Mentor David Hussey said they are thinking of different combinations this season, which includes promoting Russell at three.
KKR will take on defending champions Mumbai Indians in Abu Dhabi on September 23 as per IPL fixture which was released on Sunday.