Robbie Griffiths rates Halvorsen a classy sprinter in the making but the trainer is still guarded about the three-year-old's prospects of winning at his first attempt racing on the straight course at Flemington.
Halvorsen is set to run in Saturday's Ken Cox Handicap (1000m) against his own age with the plan to progress to the Listed Creswick Stakes (1200m) at the same track on June 22.
"I'm confident he is going well but I always get reserved about their chances in their first run down the straight, and he's back to 1000 metres," Griffiths said.
"For mine if he wins it is a bonus.
"I've found a lot of horses just need that experience before they run a peak run, but he's got the ability to win because he is coming off a win.
"We'll see how he goes there and as long as he pleases us and runs in the top four or five, then we can go to the Creswick Stakes with a bit of confidence.
"I think he's a good horse and I think he's only going to get better as he gets older. He has done everything right thus far and the form around his wins have been strong, with Hawkshot form lines and things like that."
Halvorsen made it four wins from 11 starts with a convincing victory in the VOBIS Gold Dash (1100m) at Caulfield in late April at his most recent start.
Griffiths had considered giving Halvorsen a crack at the Group One Goodwood (1200m) in Adelaide last month but shelved those thoughts, although he said it was a legitimate target for the gelding next year.
"I was half looking at that but I just didn't think he was mature enough," Griffiths said.
"And he won the VOBIS Gold race and then he just kicked out in his box and sprained a hind leg, so once that happened it was game over for The Goodwood but he probably wasn't mature enough anyway.
"I think that he's a horse that you'd look at that hopefully next year."