Additional Solicitor General PS Patwalia told the court: "We should be allowed to have free hand in the investigation. We are not going to behave unreasonably."
"There can't be any informal drawing room investigation. I want him to join the investigation which is meaningful and not to be dictated by them," the ASG added.
Senior advocates Kapil Sibal and Ram Jethmalani, appearing for Singh and his wife respectively, told the court that their clients were willing to cooperate in the investigation but they must be protected from arrest.
Sibal on behalf of Singh told the court: "I have been an MLA for 55 years, never lost any election. I have three palaces with me. I have 2,000 acres of forest land and I have been prosecuted for just six crore rupees. If we (Virbhadra Singh and his wife) are protected from arrest, we are ready to join the investigation."
Ram Jethmalani told the court that Virbhadhra Singh is sitting chief minister and his "dignity should be preserved".
The Himachal Pradesh High Court had, through an interim order on October 1, 2015, restrained the CBI from arresting or interrogating Virbhadra Singh or filing a charge sheet against him in the Rs 6 crore disproportionate assets case.
The Himachal High Court was hearing Virbhadra's plea seeking quashing of an FIR lodged against him by the CBI.
The Supreme Court in November last year transferred the disproportionate assets case against Virbhadra from the Himachal High Court to the Delhi High Court, saying the transfer was necessary "to protect the judiciary from embarrassment".
The apex court, however, did not pass any order to modify the Himachal High Court order which restrained the CBI from arresting Singh in the case.
Virbhadra Singh had moved the Himachal Pradesh High Court following CBI searches at his residences in Delhi and Shimla on September 26 last year which, he contended, were mala fide and out of political vendetta.
The case was registered on September 23 last year under the Prevention of Corruption Act against the chief minister, his wife Pratibha Singh, Life Insurance Corporation agent Anand Chauhan and associate Chunni Lal.
The case was registered after a preliminary inquiry that allegedly found that Virbhadra Singh, as union minister during 2009-2012, accumulated assets worth Rs 6.03 crore in his name and in the name of his family members, which were disproportionate to his known sources of income.