Telescope is on course to take part in a racecourse gallop next week in a last-ditch bid to enable him to make the Investec Derby field.
Sir Michael Stoute's colt was denied a run in the Dante Stakes at York this week after grazing on his legs became infected.
The only chance Telescope has of lining up in the Derby on June 1 is if he recovers in time to have a gallop next week.
"I spoke to Sir Michael yesterday and it was good news, and I spoke to him this morning and that news continues to be really good," Harry Herbert, racing manager for the owners, Highclere Thoroughbred Racing, said on Racing UK.
"We're not out of the woods, but Sir Michael hopes to have him back cantering tomorrow so he won't have missed too much and we'll be hopefully on course to work at a racecourse next week.
"That will be Sir Michael's decision, whether he's fit enough and well enough to risk him in the Derby.
"This isn't an ordinary race, you've got to be absolutely spot-on. We're excited about the horse but we'll only do the right thing by him. Sir Michael will want to run him but only if he is absolutely happy that he is over this issue fully.
"We won't know until he's had a racecourse gallop and had a serious blow afterwards. I don't know where it will be, Sir Michael will decide nearer the time."