Firebeam, second to Red Jazz in the Network Group Spring Trophy at Haydock on Saturday, could head to France for his next race.
The Highclere Thoroughbreds-owned four-year-old went down by a neck to the Charlie Hills-trained winner, having cruised up menacingly heading inside the final two furlongs.
But Godolphin Mile third Red Jazz was in determined mood and held off William Haggas' charge by a neck.
The Prix du Palais Royal over seven furlongs at Longchamp could now be an option with the trainer saying: : "He ran very well. He travelled like the best horse in the race, but he didn't win.
"Richard (Hughes) said is legs were like jelly at the end and it was soft ground, so hopefully he'll improve. There is a race for him at Longchamp on Derby day, so that could be a possibility."