The 53-year-old star was found dead at his home in Goring-on-Thames, Oxfordshire, on Christmas Day.
Michael's publicist said his family and friends had been "touched beyond words" by the "incredible outpouring of love" from fans, adding there were no suspicious circumstances around his death.
A post-mortem examination was carried out on Thursday.
Thames Valley Police said: "The cause of death is inconclusive and further tests will now be carried out. The results of these tests are unlikely to be known for several weeks.
"Thames Valley Police will prepare a file for the Oxfordshire Coroner. Mr Michael's death is still being treated as unexplained but not suspicious."