Origi has been getting used to life in the Premier League this season following his arrival at Anfield from Lille last summer.
The striker has found his first-team opportunities under Jurgen Klopp somewhat limited this season, with the forward having scored two goals and made one assist in 12 Premier League games so far this term.
However, Liverpool legend Rush has been impressed by what he has seen from Origi in recent months and is expecting to see the forward enjoy a fruitful career at Anfield.
Rush told Metro: “I think he’s got pace and I think if you’ve got pace, you’ve got a chance.
“There are some quality young players at Liverpool and Origi is definitely one of them.
“I like to see people with real pace and he’s certainly got that.
“I think he can go onto great things at Liverpool.”
Liverpool return to Premier League action this weekend with a home clash against Tottenham Hotspur at Anfield on Saturday evening.
The Reds squandered a 2-0 lead to lose 3-2 at Southampton in their most recent top-flight clash before the international break.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news