Her promising debut at Salisbury last month saw On Demand lead early on before eventually finishing sixth.
A slight injury has since then limited her work but trainer Andrew Balding, who is overseeing On Demand's progress at his Park House Stables in Kingsclere says she will be back in action soon.
"We're hoping to do a little bit of work with her a week on Wednesday and that will give us an indication of what her fitness levels are," he said.
"From that we should be able to gauge when she should be ready for an entry.
"It was very fast ground that day at Salisbury and it's not unusual for a young horse to get a little bit of jarring post-race. Happily there's nothing fundamentally, structurally wrong so we can carry on, but obviously with caution."
Reflecting on On Demand's debut performance, Balding believes there are plenty of positives to take from her performance and is optimistic of good results in the future.
"She shaped with plenty of promise and as she matures a little bit she will have the strength hopefully to see out races better.
"She got a little tired in the last half furlong having shown good speed but it was a race full of encouragement."
Sky Sports News teamed up with Great British Racing to buy On Demand in a bid to show viewers - who have since voted for her name and colours - what it takes to develop a race horse.