Champions Day at Ascot or a trip to Canada are two possible options for Encke following his creditable run when third in the Irish St Leger.
The five-year-old won the 2012 St Leger at Doncaster but his subsequent career stalled as he served a six-month ban as one of the horses caught up in the Mahmood Al Zarooni drugs scandal, missing the whole of 2013.
Now with Charlie Appleby, the Godolphin-owned Encke posted an excellent effort upon his return, when second over 12 furlongs at Goodwood, before stepping back up to a mile and six furlongs to chase home the enterprisingly-ridden Brown Panther and Leading Light at the Curragh on Sunday.
The British Champions Long Distance Cup at Ascot on October 18, for which he would need to be supplemented, is now on Encke's radar, although the Canadian International the following day remains an alternative option.
Appleby said: "He's come out the race well, we were happy with the run and he travelled well, too.
"There's a couple of options for him now, we could step him up again to two miles and look towards Champions Day or there is the possibility we could go the other way and drop back to a mile and a half for the Canadian International.
"He showed at Goodwood he is still capable of running well over a mile and a half but it's really just a matter of options.
"We wouldn't want extremes of going for him and you don't really know what the weather will be like next month.
"We would have to supplement him for Ascot and if the ground was good or just on the easy side that would be fine, but if it were to be at either extreme, we might look to Canada and ride him more positively.
"I would say Ascot is realistically the more likely option, though."
