The chances of an overseas-trained runner competing in next week's Cox Plate are fading with Afsare a notable absentee from Tuesday's Werribee trackwork session.

Afsare has been closely monitored since filling appeared in his off foreleg after galloping last week.

The Luca Cumani-trained galloper was able to work on Monday but his latest no-show at the International Horse Centre has raised serious doubts about his participation in Australia's premier weight-for-age race.

"He has got some minor filling in his off foreleg," travelling foreman Charlie Henson told Racing Victoria.

"We'll be getting the vet to have a look at him."

The Dermot Weld-trained Melbourne Cup chance Galileo's Choice was another import to stay in his Werribee stable on Tuesday.

But it was a deliberate move for the horse who will be trying to give Weld his third win in the Melbourne Cup.

Galileo's Choice has been given an easy time since arriving in Australia because he didn't cope with the long flight.

But his workload has gradually increased to coincide with the improvement in his physical condition.

"We always planned to give him the morning off today," stable spokesman Tom Daly said.

"Everything is one hundred per cent."