On Friday, the African nation's Deputy Environment and Tourism Minister, Leon Jooste, said officials had gotten an inquiry on behalf of Spears, who is pregnant with her second child.
"She has shown interest to come over to Namibia," Jooste told the Associated Press. "Nothing has been confirmed yet, but there is a definite possibility of that happening."
That day, a rep for Spears told PEOPLE there was "no truth" to the claim.
Asked if the call might have been a hoax, he said, "It is really possible."
Jooste, who is vacationing in South Africa, said he plans to look into the matter when he returns to Namibia this week – and he hasn't given up hope: "I am actually going to call and invite them to see if they would like to come."
Spears, 24, and husband Kevin Federline, 28, are parents to 9-month-old son Sean Preston. Their second child is due in September, Spears told Matt Lauer in a Dateline interview that aired Thursday night.
Brad Pitt and Angelina Jolie recently boosted Namibia's appeal to privacy-seeking parents-to-be: After their daughter, Shiloh Nouvel, was born in the country on May 27, Pitt said the baby's birth was "truly peaceful" and that they "had top-notch medical care."
Added Jolie, "We want to tell the world how magnificent this country and the people are."