The eight-year-old, owned by Barry Connell, landed the Close Brothers Novices' Handicap Chase in 2017 and is likely to go for the Brown Advisory and Merriebelle Stable Plate this time round.
Tully East has been lightly-raced this term and shaped well when third of 20 behind Patricks Park at Leopardstown last weekend.
"He came with a couple of small scratches but nothing to write home about. All's well with him," said Fleming.
"He'll go straight to Cheltenham now. He'll have a couple of entries, but I'd say the two-five handicap would be the main aim."
As You Were is set for the Ballymore Novices' Hurdle at the Festival after drawing 25 lengths clear of the third when only beaten half a length by Ballyward at Naas two weeks ago.
"He run a lovely race at Naas. They pulled 25 lengths clear of everything else, so it was a fair run," said Fleming.
"We were unlucky to bump into one like that in a maiden.
"He'll not run again. He'll go straight for the Ballymore now."
Foxrock is also set to have his next run at Cheltenham after Fleming decided against running in a hunter chase at Punchestown on Sunday.
"He had a hard race at Thurles and we decided we'd miss this weekend," said the Curragh handler.
"I'm not sure if he'll run before Cheltenham but we'll have him as right as we can for there."
Foxrock is prominent in the market at around 7-1 for the Foxhunter Chase.
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