The former Leeds keeper, signed last month after being released by The Whites, has been given time off by the Glasgow club.
Celtic boss Martin O'Neill said: "We will give him time and see how that develops, then have a look at it.
"We signed Danny Milosevic until the end of the season when we knew Magnus Hedman was going to Italy.
"He signed a contract, but he has a few personal problems that he wants to get resolved."
Milosevic was signed by Celtic on January 29th after impressing on trial, but the Aussie is now back in England.
He had impressed on trial sufficiently to be seen as ideal back-up to Scotland international Rab Douglas.