The 26-year-old batsman, who made 352 runs in 14 matches during the Indian Premier League 2020 season in the UAE, was holidaying in Goa before joining the team and his positive test report came two days ago, according to a report in Dainik Bhaskar.
The franchise did not respond to calls from IANS asking for confirmation.
Rana is under observation and undergoing quarantine at the team hotel.
The left-hander has played 60 matches in his IPL career, which began in 2016. He has so far scored 1,437 runs at an average of 28.17 and a strike rate of 135.56.
Rana had been in form in the recent Vijay Hazare Trophy one-dayers, scoring 398 runs in seven matches at an average of 66.33 with a strike rate of 97.79. He was the tournament's fifth-highest run-getter.
The Delhi batsman, who also opened for KKR during the last season, has not been seen in practice sessions even as other players have been attending practice.
Skipper Eoin Morgan, Shubman Gill, Kamlesh Nagarkoti, Shivam Mavi, Andre Russell, Dinesh Kartik and Sunil Narine have all been doing practice sessions.