Murray will attempt to defend his WBC silver middleweight belt against Italian Domenico Spada in Monte Carlo on October 25, and if the St Helens fighter comes through that bout, Harrison has revealed that he has high hopes in a meeting with one of the sport's pound-for-pound kings.
At the pre-fight press conference earlier on Wednesday, Harrison said: "He's trained really hard for this fight. We've been over to Ireland for sparring and it's gone really well. We've trained a little different for this fight so hopefully you'll see something a bit special.
"This is intended as a warm-up for Golovkin. When we fight Golvokin, everyone thinks that Martin is going to lose, but he won't lose. He has the confidence and skills to beat him, even though Golovkin has the power.
"We know that we still have a fight with Spada, but after him, we will go on to win the world title against Golovkin."
Harrison has been a part of Murray's team since his professional debut in 2007.