A long-awaited report on a proposed second supervised injecting room in Melbourne has been handed to government, but it isn't being released immediately.

Former Victoria Police commissioner Ken Lay delivered his final report on a possible trial in the city's CBD to Mental Health Minister Gabrielle Williams on Wednesday, Premier Daniel Andrews confirmed.

Mr Andrews has not read or been briefed on the report and said it would be considered by cabinet before being released, although there is no deadline.

"I'm not going to put a date on it, but we'll do that as quickly as we can obviously (and) we'll have more to say at the appropriate time," he told reporters on Thursday.

A medically supervised injecting room trial in the CBD has been under consideration for several years, with the state government buying a building near Degraves Street.

The first North Richmond injecting room was opened in June 2018 as part of a trial and made permanent in early May after a review found it safely managed almost 6000 overdoses and saved 63 lives.