Mawj could be seen next in the Sky Bet Lowther Stakes at York on August 18.
The Saeed Bin Suroor-trained filly lost little in defeat at Royal Ascot when second to Aidan O'Brien's Meditate in the Albany Stakes, with the winner and runner-up looking two youngsters of real potential.
A daughter of Exceed And Excel, Mawj had made a winning start to her career at Newmarket in May.
"The horses are running well. We had four winners on Saturday," Bin Suroor said.
"Mawj is doing good, she came back well. I would like to see how she is in a week's time. I think there is a race for her at York.
"I want to see how she is. She is tiny – not a big filly – and we don't want to over-do her. We have to look after her, but she is a nice filly."
Bin Suroor also confirmed stable star Real World on course for the Coral-Eclipse at Sandown on Saturday, having twice been second at the top level to Baaeed this season – mostly recently in the Queen Anne at the Royal meeting.
"Real World will go to Sandown. We will look for a Group One for him," he said.
