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(CNN)An American couple who say they have been stuck in Mexico for weeks because officials there won't provide a birth certificate for their son believe a resolution could be close.

Haseeb and Christy Amireh, of San Jose, California, had a baby with the help of a surrogate mother in the Mexican city of Villahermosa, in the southern state of Tabasco.

Their son, Grayson, was born on April 16. The Amirehs were present at the birth, and everything to that point had gone according to plan.

But since Grayson's birth, Tabasco state authorities have not provided the parents with a birth certificate.

According to the couple, Mexican officials told them laws regulating surrogacy had changed and they could no longer get the documentation to return to the United States.

On Friday, the Amirehs said a resolution may be close, but declined to talk about specifics.

"The momentum to be able to go back home is quickly building," Haseeb Amireh said. "We may have good news as soon as this weekend."

The couple set up a fundraising website to help with legal...