In a statement released on Wednesday, Waller said he had discussed all options with the mare's ownership group and it had been decided there was insufficient time to properly prepare Verry Elleegant for the Arc.
Instead, she will continue her career in Australia with Waller earmarking the Winx Stakes (1400m) at Randwick in August for her return.
"Whilst running her in the Arc would be a dream come true for all of us, we just felt that it would come around too soon to enable her to have a proper spell and be fully prepared in Australia for this assignment," Waller said.
"However, a trip to Europe a little later in the spring is still strongly on the cards, providing she returns to the form she showed in the spring when dominating the Melbourne Cup."
Waller has identified a Group 1 fillies and mares' race over 2400m on Champions Day at Ascot as an ideal international target and says the October 15 meeting is "one of the most prestigious race days in the world and a worthy stage to showcase her talents".
A shot at back-to-back Melbourne Cups is also in the mix, depending on Verry Elleegant's form.
"It is likely that she will have three runs in Australia in the spring with the Winx Stakes, the Chelmsford (Stakes), the Kingston Town (Stakes) and The Underwood all being considered, prior to a decision being made on a Melbourne Cup defence, or a trip to Europe," Waller said.
A rising seven-year-old, Verry Elleegant has won 11 Group 1 races and banked more than $14.8 million in prizemoney.