The 14-time Grand Slam winner has been sidelined since withdrawing from the French Open in May.
His coach and uncle, Toni, was enthusiastic after the 30-year-old's practice session with Andy Murray in Manacor, Mallorca.
"We began to intensify his training in order to be ready in time for the first round," Toni Nadal said on Thursday.
"Training with Andy Murray was a really hard first time with another top player and we are happy. Things worked out well. In Rio we will start training with the maximum-level players and see how Rafael will respond to the difficulty of the competition," he added.
"There are doubts about his game. I believe that is normal - these are the same questions we've always had after a period of inactivity. Starting with the Olympics is not easy but if we are lucky in the draw, he can improve step by step."
Nadal won gold at the 2008 Beijing Olympics, but missed the London Olympics four years later because of a knee problem.
He is expected to be Spain's flag-bearer at the opening ceremony on August 5, and will compete in the singles and the mixed doubles with French Open winner Garbine Muguruza.