Phoenix Tower and Famous Name could be in line to run in the International at York later this month.
Both runners would be seeking a first success at Group One level should they contest the 10-furlong event on August 19.
Phoenix Tower, who is trained by Henry Cecil, was last seen when finishing just a short head behind Mount Nelson in the Eclipse, while Dermot Weld's Famous Name was only beaten a head in the French Derby.
"We are undecided about the International and Phoenix Tower and possibly Famous Name could be heading for that, but Twice Over won't run," said Teddy Grimthorpe, racing manager to Khalid Abdullah, who owns both horses.
Cecil also handles Twice Over, winner of the Prix Eugene Adam last time and the Craven Stakes earlier in the season.
The Observatory colt is a possible for the Prix Guillaume d'Ornano at Deauville on August 23 but connections will make a decision on his participation later in the month.
Grimthorpe added: "He has the option of a race in France but we will see how he is. He came back fine from his last run in France but has had quite a long season."