Rogic has become a key player for Brendan Rodgers Celtic side over the past two seasons despite a slow start to his time at Parkhead.
The 26-year old has long been linked with moves away from Glasgow and the Scottish League including a rumoured transfer to Premier League giants Arsenal last season.
However, the mercurial midfielder committed his long term future with the Hoops when he signed a five year deal with the club in May 2018.
Moore, who also played in the Premier League with Newcastle United as well as a stint in Germany's Bundesliga with Borussia Monchengladbach, told the Herald Scotland he believes Rogic will eventually make a move to England or Europe.
“A lot of people didn’t believe Tom could come to Scotland and do well for Celtic,” he said. “I was always convinced he would.
“I knew what was there and what he had to offer. He is very good in his area. He is good at creating opportunities, he is good at scoring goals, he is good at assisting.
“I am really happy for Tommy. He has done really well. He has been a great player for us, for the national team as well. But these are things that I kind of thought would happen. I wasn’t really surprised.”
Moore said he believes Rogic made the right decision to stay with Celtic for the time being as it is a perfect place for him to further hone his skills and maximise his development as a player.
"Moving on probably wasn't right at the time (last season)," Moore said.
"From Celtic’s point of view, they they have protected their asset until 2023.
"He may well go in that period of time. But they will get money for him if he does. There may come a time where he does move on.”
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