Celtic signed the winger from Melbourne City last summer but he has made one solitary appearance from the bench this season and that too for a minute.
Tilio is struggling to even get into matchday squads at Celtic and has been firmly on the fringes of Brendan Rodgers’ first-team plans.
The 22-year-old has seven international caps for Australia and former Socceroos and top flight star Moore indicated that he is worried about the winger.
He stressed that Tilio needs to get himself out of Celtic as he is a bright prospect for Australia and needs to play more football moving forward.
Moore urged the Australia international to try and find himself a new club in the January transfer window.
He said on the Go Radio Football Show: “Tilio needs to get himself another football club.
“I am saying that because he is an Aussie boy and he has a chance of having an impact with our national team.
“Like any player, he needs to get himself in a situation where he is playing football and unless several players fall over, it is not going to happen at Celtic.”
It remains to be seen whether Celtic receive offers for Tilio when the window opens in just under a month’s time.