Ms Dingley, an experienced hiker, was last seen on Pico Salvaguardia in the Pyrenees, on the border between France and Spain, on November 22.
She and her partner Dan Colegate left England in 2014 for the adventure of a lifetime, which was to last 12 months but spanned six years.
The 37-year-old sent Mr Colgate a selfie from the 9,000-foot Safeguard Peak the day she went missing and hasn’t heard from since.
French police say they are currently analyzing the bones to try to confirm if they are human remains.
A mountain runner sounded the alarm on Friday around 2 p.m. after discovering what he believed to be the remains of a body. Spanish police visited the area and alerted their French counterparts after discovering the place was just across the border.
French officers have now taken over the investigation to try to confirm whether the bones are human and, if so, to whom they belong. Spanish police sources said the bones appeared to be human.
A source from the Civil Guard said: “A mountain runner found what could be human bones just across the French border at Puerto de la Glera. They appear to be human remains, but it will now be up to the French police to analyze them. . “
Another Spanish source said it appeared “90 percent certain” that it was human remains.
Specialized officers from Spain and France carried out several searches in the vicinity of the Puerto de la Glera hiking trail. The search was halted in December due to heavy snowfall and resumed last month.
Mr Colgate said in a recent interview with the BBC that he “could no longer agree” with the idea that Ms Dingley had been in an accident. He said: “The research has been so prolonged and so intense that as far as I’m concerned, the likelihood of an accident is now lower than the likelihood of a criminal act. ”