Earlier, the apex court had granted Kumar protection till May 24.
Kumar has moved the court with a fresh plea as lawyers in West Bengal have gone on strike and courts are not functioning.
A vacation bench comprising Justices Arun Mishra and M. R. Shah said, "All mentioning (of petitions for urgent hearing) are allowed. The petitions would be listed tomorrow."
Kumar, in his plea, has said his protection from arrest be extended till the lawyers' strike in the state ends.
On May 17, the Supreme Court had vacated the interim protection from arrest by the Central Bureau of Investigation granted to Kumar on February 5.
The investigating agency has accused Kumar of tampering with the evidence in the chit fund scam to shield powerful politic.
The court had expressed concern over the manner in which the chit fund scam case has panned out, while vacating its February 5 order.
A bench comprising Chief Justice Ranjan Gogoi, Justice Deepak Gupta and Justice Sanjiv Khanna had said: "We would withdraw the protection given to Mr. Rajeev Kumar, former Commissioner of Police, Kolkata, vide our order dated February 5, 2019 restraining the CBI from arresting him and thereby, leave it open to the CBI to act in accordance with the law."
The court, however, granted seven days to Kumar for appropriate legal remedies. "At the same time, we direct that the interim order dated February 5, 2019 would continue for a period of seven days from the date of pronouncement of this order to enable Kumar to approach competent court for relief, if so advised," it said.
( With inputs from IANS )