The former Leicester City defender helped the Royals reach the play-offs last season and is a former England youth international.
If Celtic fans were unsure about Moore, they should consider that he is backed by one of the best defenders of the late 90s, Jaap Stam.
Stam has been Reading boss since the summer of 2016, and made Moore one of his very first signings.
Here is a look at what Stam said about Moore when he signed him.
He told Get Reading: "Liam is the type of defender who can play high up the pitch, because he has pace and he can cover distances quickly should the opposition play long balls over the top or try to get in behind the back line.
"He is comfortable on the ball and can play it out from the back, he is an aggressive defender and good in one-on-one situations. I’m really pleased he has joined our squad at Reading.”
Moore is under contract until 2020 and Reading are under no pressure to sell.
Celtic could hope to persuade him, with the option of challenging for trophies, considering that Reading's start to the season has been poor.
If they do manage to pull it off, then Stam's words should be encouraging to all involved.