The 21-year-old will be based at the club’s Academy in Kirkby.
Hardy made his debut as a substitute in Sunday's U23s’ fixture away at Manchester City, the club where he played his youth football.
The Wirral-born striker made the switch to Brentford in 2017 and went on to score 40 goals in 80 appearances for the Championship club’s B side, finishing top scorer last season.
Liverpool Academy manager Alex Inglethorpe believes the player will add extra competition to the striking ranks at U23 level.
He said: “Joe is a good goalscorer and we think he can have an impact on our U23s, and from there it’s up to him.