Denise Pikka Thiem disappeared in April while hiking the Way of Saint James pilgrim trail in northwestern Spain.
Police had resumed their search for her on Thursday near the northern town of Astorga where she was last seen.
Three hundred officers with dogs and a helicopter were deployed in the operation, which focused on wells.
"A person has been arrested and the search has been suspended for the moment," a police source told AFP late Friday, without giving further details.
Spanish newspapers said Saturday that police have found a body on the suspect's property, although authorities could not immediately be reached to confirm the reports.
"The body of the American pilgrim who disappeared on the Way of Saint James on April 5 was found on Friday on the property of the main suspect, in Astorga," the daily El Pais said.
"It is a very large area and ideal for hiding a body," the ABC newspaper said.
The El Mundo daily said: "Police have therefore closed the case. The suspect would the only person charged in the death of Denise."
Hundreds of thousands of tourists and Roman Catholic pilgrims hike the Way of Saint James, known in Spanish as the Camino de Santiago, each year, staying at hostels on their way to the northwestern city of Santiago de Compostela.
Thiem has not been heard from since April 4 when she sent a message to a friend saying she was at a point on the trail near Astorga.
The Way of Saint James is hiked by hundreds of thousands of tourists and Roman Catholic pilgrims who stay at hostels on their way to the northwestern city of Santiago de Compostela.
Spain's Prime Minister Mariano Rajoy has written to Thiem's parents in Arizona, saying he "understands the pain of a family that does not know where their daughter is."