Encke could embark on the Ladbrokes St Leger trail with a run in the bet365 Gordon Stakes at Glorious Goodwood on July 31.
Mahmood Al Zarooni's colt looked a smart prospect in winning a Newmarket maiden last October but did not reappear again until earlier this month, when he narrowly landed a handicap at Sandown.
"He won, but he was a little short of work and was very green," said Godolphin racing manager Simon Crisford.
"He has the option of running in the Gordon Stakes or a mile-and-a-half handicap for three-year-olds at the meeting.
"He's progressive and hopefully a St Leger type of horse, but he has got to prove himself."
One of the premier trials for the final Classic of the season, the Gordon could include Frankel's younger brother Noble Mission.
He was a close second to Sir Henry Cecil-trained stablemate Thomas Chippendale in the King Edward VII Stakes at Royal Ascot.
Teddy Grimthorpe, racing manager for owner Khalid Abdullah, said: "Noble Mission came out of Ascot well and he goes for the Gordon."
