Encke is unlikely to run again this season despite recovering from the setback that ruled him out of last Saturday's Racing Post Trophy at Doncaster.
Mahmood Al Zarooni took his charge out of the Group One contest on the morning of the race after he went lame.
However it was only a minor setback and Encke will head out for his winter break in good health.
"He's fine now. He was just lame one day before the race and he was not walking right the night before," said the trainer.
"We weren't 100% happy so we decided to scratch him. These things happen in racing, but he is fine now. It was only something small.
"I will speak with Simon Crisford (Godolphin's racing manager), but I think we will leave him for next year."