After winning the Victorian Oaks last week Barynya's owners Lloyd and Judy Whish-Wilson were told of a possible invitation to race the filly in the Harness Jewels series in New Zealand.
While nothing is set in concrete the filly's owners must now decide whether to consider the overseas option or persist with pans to tackle the Victorian Sires Stakes series next month and then on to the Breeders Crown.
Barynya won the Tasmanian oaks before heading to Melton two weeks ago to contest the Victorian Oaks series running third in her heat before giving her rivals a pacing lesson in he final at Melton last Friday night.
"I heard from Lloyd (Whish-Wilson) yesterday and he told me that there might be an invitation offered to go to New Zealand but I am already in two minds about that sort of trip," Eaves said.
"There is plenty to aim for just across Bass Strait without chasing stuff overseas but we will have a good talk about what's on offer and then make a decision," he said.
Eaves said Barynya is the best he has trained.
"I've had some really good horses over the years but the more this filly has raced the better she's become so I am now content to say she's the best I've trained," he said.
Eaves trained another star filly in Kanungra Koala that won a NSW Oaks and was beaten a half neck by Nellie Robins in the Victorian Oaks three starts later.
Barynya will spent the next few days in the paddock but will resume full training next week.
By Peter Staples