The couple have hit a rough patch because the 38-year-old singer, son of legendary Spanish crooner Julio Iglesias, is not rushing into marriage, reported the Huffington Post.
"Anna is getting tired of waiting for him to decide if he wants to marry her or not. They've been together for so long, she feels like it's never going to happen. She is ready to move on," a source said.
Despite rumours in May that Iglesias and 32-year-old Kournikova were due to tie the knot, his management team insisted that they have "no intention" to marry in the near future.