The Siyouni colt could attempt to provide the Marlborough handler with back-to-back wins in the six furlong Group Two prize on August 21, having captured the Knavesmire feature 12 months ago with Threat.
Mohawk King made the perfect start to his career when overcoming a slow start to come out on top on his debut at Ascot last month.
Hannon said: “I’m looking at the Gimcrack for Mohawk King. He missed the gate at Ascot, but he was very strong at the line and did it in a pretty good time.
“He came from the Tattersalls Craven Breeze Up sale so we’ve not had him that long. His work had been very good going forwards into that first race.
“He seems to have plenty of speed and I see him being a Gimcrack then Middle Park type of horse.”
The Tattersalls Acomb Stakes at York 48 hours earlier is one of two potential Pattern-race targets for stablemate Chindit, along with the Champagne Stakes at Doncaster.
Having struck gold first time out on Town Moor, the son of Wootton Bassett followed up with an impressive victory in the Listed Pat Eddery Stakes at Ascot.
Hannon said: “I think we will be looking at either the Acomb or the Champagne Stakes for Chindit as we might have a few others for the Solario at Sandown.
“He hit the line strongly and won the Listed race with authority at Ascot, which is lovely to see a two-year-old do.”
Hannon does not expect to have his hand forced to run Mohawk King and Chindit against each other this season, with both appearing to want different trips.
He said: “Whereas Mohawk King is more of a speed horse that will race over six furlongs, Chindit is very much a seven-furlong to a mile type of horse.
“Chindit has come out of that race extremely well and we are happy where he is at at the moment.”
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