Lokpal is an apex body to inquire and investigate into allegations of corruption against public functionaries.
A former chief justice of the Chhattisgarh High Court, he had been in the AIIMS Trauma Centre, which has been converted into a dedicated COVID-19 hospital.
Lokpal member Ajay Kumar Tripathi has been put on a ventilator and his condition is critical but stable.
Justice Bhosale had sent his resignation to President Ram Nath Kovind on Monday, sources said.
A senior Personnel Ministry official said the Lokpal is likely to move out of its five star hotel temporary office at The Ashok Hotel in Chanakyapuri by January end.
There is the limited scope of contempt petition and the NGO can file a separate petition seeking directions for effective functioning, it said.
The opposition party also alleged that till October 31, 2019, 1,116 corruption complaints were received but the preliminary inquiry was not started in anyone.