Police apprehended the pair, aged 33 and 30, after neighbors noticed them driving slowly around the area in a red Fiat Punto, the Sun reports.
They reportedly had detailed maps and aerial photos of Stone's property in east Devon.
"I'd like to thank everyone for their concern but I'm absolutely fine and getting on with life as normal while the police continue with their inquiries," the singer said in a statement Wednesday.
And reps for Stone adds that the "police are keeping her updated with developments."
Detective inspector Steve Parker said in a statement: "The men had information and items that lead us to suspect that they may have intended to commit a criminal offense."
Stone, 24, has an estimated personal fortune of some $14 million, the paper says.