Although plans remains fluid, the seven-furlong Group Three prize is one of a number of options under consideration for the Roger Charlton-trained daughter of Frankel.
The Khalid Abdullah-owned three-year-old, who provided her sire with a first Pattern-race winner as a stallion in the Princess Margaret Stakes last year, has not been seen since finishing fifth on her seasonal return in the 1000 Guineas.
Assistant trainer Harry Charlton said: "She had a setback after the Guineas, but she is back in training and in work.
Fair Eva should be back in action by the middle of next month
"We are looking, if everything has gone as we hope, for a run in the middle of September. There is the Sceptre Stakes at Doncaster and the Rosemary Stakes at the end of September. Those are the sort of races we are looking at.
"Every small step with her at the moment is a good one."
Time Chaser, who is a full-sister to dual Group Two winner Time Test, is likely to be kept to handicap company on her next start as she bids to maintain her perfect record and make it four wins from four.
Charlton added: "Time Chaser looks like she is heading to Haydock on September 9 for a handicap there.
"I think with her handicap mark at 91, we would still like to take a pop at 105-rated horses in a handicap. She is obviously progressing and is in great nick."