Tiberian's connections will need to decide whether to give the partly Australian-owned stayer another run before he travels to Melbourne after his strong win at Deauville on Sunday.
Australian Thoroughbred Bloodstock bought a 50 percent share in Tiberian earlier this year and the French-trained galloper made it three wins from four starts since the purchase in the Group III Haras de la Pomme Prix de Reu (2400m) on Sunday.
Jockey Olivier Peslier had Tiberian on the pace throughout before holding off the Andre Fabre-trained Doha Dream to score by a short head.
Tiberian's win prompted Sportsbet to trim his Melbourne Cup price to $34.
Australian Thoroughbred Bloodstock owner Darren Dance said the post-race reports from the stable indicated Tiberian had something in hand at the finish.
"We went into the race reasonably confident that he'd win but it's good when do," Dance said.
"He had a lot of weight, 61.5kg, in a Group III over 2400m on a firm track, which we know he probably prefers.
"He hit the line with a bit in reserve. The jockey said he only hit him once and he always felt he was going to win the race."
Dance said Tiberian would get a run in the Melbourne Cup with a probable 54kg handicap on his current form but trainer Alain Couetil was considering whether to run the stallion again before he enters quarantine on September 28.
"We'll let the trainer see how he pulls up but he could have one more (run) before he goes into quarantine," Dance said.
Tiberian will head to Australia in the second shipment of international runners, meaning he will not have a local lead-up race before the Melbourne Cup.
Dance said that approach almost achieved the ultimate result with Heartbreak City last year, who narrowly fell short of Melbourne Cup victory when second to Almandin.
"We'll do the same programme as we did with Heartbreak City and only have one run here," Dance said.
"My horses generally go straight back (to Europe) after the Melbourne Cup because there are a lot of races for them in Europe."
