The son of Midshipman , who has one win from 10 career starts, was third in the Besilu Stables Fountain of Youth (gr. II) and unplaced behind American Pharoah in both the Kentucky Derby Presented by Yum! Brands (gr. I) and Belmont Stakes Presented by DraftKings (gr. I) before finishing fourth and last behind Travers hopeful Texas Red in the Jim Dandy (gr. II) July Aug. 1 in his most recent start.
Triple Crown winner American Pharoah also is under consideration for the race. If he runs, the Travers purse jumps to $1.6 million from $1.25 million.
Zito said he was pleased with Frammento's most recent workout, a half-mile breeze in :48 4/5 Aug. 15 at Saratoga. The time was the third-fastest of 75 moves at the distance.
"He worked extremely well the other day and hopefully he'll come back and do the same thing," Zito said. "We'll always keep trying. It's a very interesting race for a lot of money. We'll see what the deal is.
"He worked very, very, very, very well; the best he's worked. He went :23 and change, :23 and change, and he was up in :59 and change. You say to yourself, 'Why does he have to be 40 lengths behind (in his races) when he works like that?' But, that's his style."
The late-running colt will breeze again this weekend, depending on the weather. Zito has yet to settle on a jockey for the Travers; Frammento has had seven different riders in 10 starts.
"The gates opened up and he broke on top in the Jim Dandy, and the next thing you know he was so far back," Zito said. "He wasn't disgraced there. It was only a four-horse race, but they were top horses in there. This extra distance, the mile and a quarter (of the Travers), you never know. We're always going to try."