Already eligible for the $3 million Big Dance, the gelding turns five in the new season and Sterling Alexiou said that opens up other rich options like the $1 million Five Diamonds Prelude and $2 million Five Diamonds as well.
The form guide shows Grebeni hasn't trialled officially but Alexiou said he has had a 900m unofficial trial at Rosehill last Tuesday ahead of the Catanch's Jewellers Handicap (1400m).
"He seems to be coming up quiet well, he's a horse that although he can run well first-up he seems to improve off it,'' he said.
"Last preparation he resumed in the Silver Eagle which was only 1300m. I imagine whatever he does on Saturday he'll improve on.
"He'll probably only have the three runs, because he's turning five there's the Five Diamonds and winning the Goulburn Cup he's eligible for the Big Dance."
Those three runs will see Grebeni, who won successive Randwick miles in December before a spell, follow Saturday's resumption with the Group 3 Hawkesbury Cup (1600m) in two weeks and the Listed Scone Cup (1600m) another two weeks later – both races also carrying Big Dance eligibility.
Alexiou, who co-trains with Gerald Ryan, said expect to see Grebeni, $11 with TAB on Thursday, conservatively ridden from a wide gate and to be finding the line with purpose.
He's yet to win first-up but is unbeaten in three second-up attempts.
"The barrier will probably see him get back but he's not a horse that has abundant gate speed so he'll settle in the second half of the field,'' he said.
"We'd like to see him relax, travel well, and finish it off. In terms of fitness he's probably a little bit behind where he normally is but he's fit enough to run well.
"He's nearly got a 50 per cent win strike rate and it takes a very handy horse to do that. Some might say he's been well placed but horses have still got to go out there and win."
The stable is sweating on three-year-old General Salute gaining a start in the Petaluma Handicap (1200m) as Alexiou sees the race as an ideal chance for the gelding to notch a second career win.
He wrapped his spring with a Listed placing in the Brian Crowley Stakes at Randwick and resumed with a sixth in the Listed Darby Munro (1200m), after going back from a wide gate and running on, behind Brave Mead.
"He's finally drawn a gate, he's a horse that's raced without luck and bad barriers,'' he said.
"The inside draw is a big tick for him. He seems to race a lot better away from Rosehill at Randwick. When he got to Randwick he ran a much improved race before he went out.
"He's got his fair share of ability, we've seen glimpses of it. We'd like to see things go his way for a change."
General Salute will progress to the Group 3 Hawkesbury Guineas (1400m) if he wins or is right in the finish on Saturday.
Sterling Alexiou on Pajanti (race 3): "She won well first and second-up, through lack of races she had to take a step back to six furlongs on a track that didn't suit her. If she can settle in the first half I'm sure she can run a good race."
On It's A Wonder (race 3): "I thought she did a good job to win the other day off an awful trial, I don't think there's any other way to describe it. She has a distinct disliking for racing in amongst horses and that's probably why she performed so badly in the trial. A mid to wide-ish gate for her will do her the world of good. She's got a very good turn of foot and she'll be very strong late."
All the fields, form and replays for Saturday's Randwick meeting
