Steinbeck is pencilled in to make his return in the Abu Dhabi Irish 2000 Guineas after pleasing in a racecourse spin on Monday.
Aidan O'Brien's charge, who finished fourth in the Dewhurst last year, suffered a setback in March that ruled him out of the Newmarket Guineas last weekend.
He pleased connections in a gallop and is due to return to the Curragh on May 22 for the first Irish Classic.
Investec Derby hope Jan Vermeer was also in action, along with Lillie Langtry and Rip Van Winkle, while O'Brien is hoping to get all three back on track in the near future.
"We were pleased with the horses that cantered up after racing," he said. "Hopefully Rip Van Winkle will now head to the Queen Anne Stakes at Royal Ascot, Lillie Langtry could have her first start in the Irish 1000 Guineas (and) Steinbeck for the Irish 2000 Guineas.
"We have not decided where to start Jan Vermeer yet."
Blanco to lead O'Brien team
Cape Blanco heads a three-strong Aidan O'Brien challenge on the Derrinstown Stud Derby Trial at Leopardstown on Sunday.
The Ballydoyle handler has trained six of the past 10 winners of the Group Two contest, which has thrown up several subsequent Epsom Derby winners, including O'Brien's Galileo (2001) and High Chaparral (2002).
Cape Blanco is as short as 12-1 for Epsom glory next month.
His stablemates At First Sight and Midas Touch have also been entered, while Jim Bolger could be represented by Reiteration and Shintoh.
Dermot Weld's Address Unknown and the Kevin Prendergast-trained Famous Warrior complete the seven possibles.
Rocket one of seven in Vase
Aidan O'Brien's Rocket Man is among seven runners in the MBNA Chester Vase tomorrow.
The Ballydoyle handler has saddled Soldier Of Fortune and Golden Sword to win two of the past three renewals, and this year's representative arrives on the back of a Curragh maiden win last month.
David Wachman's Icon Dream joins him on the trip from Ireland, while Critical Moment and Morana cross swords for the second time this season after claiming third and fifth finishes respectively in the Craven Stakes.
Chink Of Light, Ted Spread and Tominator complete the line-up.