The event was due to take place in 2018 and is held every 10 years.
In 2008 it was overshadowed by several leaders who boycotted it in protests to gay clergy.
The presiding bishop of the Episcopal Church in the US, the Most Rev Katharine Jefferts Schori, claims the Archbishop of Canterbury, Justin Welby, would not call the conference.
According to The Irish Times, she said: "[It is] very clear that he is not going to call a Lambeth until he is reasonably certain that the vast majority of bishops would attend."
She said the next meeting "needs to be preceded by a primates meeting at which a vast majority of primates are present".
She added: "As he continues his visits around the [Anglican] communion to those primates, it's unlikely that he will call such a meeting at all until at least a year from now or probably 18 months from now.
"Therefore, I think we are looking at 2019, more likely 2020, before a Lambeth Conference."