Police officers investigating the case said they would record statements of Asha, who might be able to reveal the reason behind her 56-year-old daughter's suicide.
A police official said they had recorded statements of Asha's sister Usha Mangeshkar, maid Dipali Mane and driver Vijay.
"Close family members have not been questioned yet since they are still in a state of shock," the police official said.
The officer said police would soon record the statements of Asha, her elder sister and legendary singer Lata Mangeshkar and Varsha's former husband Hemant Kenkre.
Police officials, however, said the Belgian pistol, with which Varsha allegedly killed herself, was registered in the name of Anand, Asha's youngest son and it was kept safely in the house.
Varsha was Monday found dead with two bullet injuries in her head.
She was the second of the three children of Asha and Ganpatrao Bhosle and stayed mostly with her mother in the posh Prabhu Kunj building in Mumbai.
Police suspect that she committed suicide Sunday night, but also said that the neighbours did not hear any gunshot.
Varsha's viscera sample has been sent for test.
Police sources said the woman's post-mortem report confirmed she died of haemorrhagic shock due to bullet injuries.
Three loaded cartridges were found in the pistol.
Varsha, who used to work as a freelance journalist, was divorced from sports journalist Hemant Kenkre.
She wrote columns for web portal Rediff.com, The Sunday Observer and the Gentleman magazine, among other freelancing projects.
She had also sung songs for some Hindi and Marathi films and performed in some concerts with her mother.
She was depressed for many years and had tried to commit suicide in 2008 and 2010 by consuming sleeping pills.