The Sea The Stars filly, trained in Chantilly by Alain de Royer-Dupre, has been prominent in the betting for the Classic since winning the group three Prix Cleopatre at Saint-Cloud on May 17.
Shamkala still holds an entry in the Oaks but connections of the Aga Khan-owned three-year-old are keen to run her in the French equivalent at Chantilly a fortnight later.
Georges Rimaud, French racing manager for the Aga Khan, said: "Things are evolving on many things, and Epsom is still in our thoughts. But the principal goal for the filly is the Prix de Diane [French Oaks]."
Aidan O'Brien could have up to five runners at Epsom - staged this year in memory of Sir Henry Cecil - spearheaded by Marvellous, winner of the Irish 1,000 Guineas at the Curragh last Sunday.
O'Brien said: "Bracelet [well beaten in the 1000 Guineas at Newmarket earlier this month] is a possible. There's also Tapestry, Marvellous and I suppose the filly [Dazzling] that ran in the trial in Navan. We'd be looking at four or five possibles."
Dermot Weld - trainer of Tarfasha, accomplished winner of the Group Three Blue Wind Stakes at Naas - will consider alternatives if the ground deteriorates.
He said: "I'm very happy, but she's a fluid-moving filly and likes top of the ground. If it turned up soft I don't think we'd run. She'd then go to Royal Ascot or the Irish Oaks."
Frankie Dettori was encouraged by Amazing Maria when the horse cantered at Epsom yesterday.
Ed Dunlop's filly looked impressive in the group three Prestige Stakes at Goodwood last season but faces the Oaks without a preparatory run.
Dettori said: "When you miss a trial it's important to get her here [to Epsom] and stretch her legs. The rain's quite good, she raced on it before and she likes it."
Stablemate Island Remede also worked at Epsom to confirm her place in the line-up, while Oaks ante-post favourite Taghrooda engaged in a solid piece of work.
John Gosden's filly - like Tarfasha, owned by Sheikh Hamdan Al Maktoum - is thought likely to appreciate the mile-and-a-half trip.