The 20-year old signed a three-year deal at the King Power Stadium in September and he has made 14 first-team appearances for the Foxes this season.
For the remainder of the season he will join up with Uwe Rosler's Brentford who are currently seventh in League One, although there is just four points between them and league leaders Swindon.
If his registration is confirmed by the Football League in time, Moore could make his debut for the Bees when they host Walsall on Saturday.
Brentford sporting director Mark Warburton told the club's official website: "Liam is a player I have tracked and monitored for the last two to three years.
"He has come through the same youth system that produced Jeffrey Schlupp, who I am sure Brentford fans will remember.
"Liam has had an excellent academy education and he has developed in to a fine young defensive player.
"He is comfortable both in central defence and at right-back and also, crucially, in defensive midfield.
"He has already achieved a lot this season, playing in the Championship with Leicester, and other clubs were looking at him. We are delighted he chose Brentford."