Other media have singled out Portugal or the Dominican Republic as possible destinations for the former monarch who abdicated in 2014, but his exact location has yet to be pinned down.
The royal palace has refused to reveal where Juan Carlos is living, saying he will announce it himself if necessary.
Pro-monarchy newspaper ABC wrote that the 82-year-old boarded a private jet on Monday from Vigo in northwestern Spain along with one aide and four bodyguards.
Seven hours later, the plane landed at a business airport in the capital of the United Arab Emirates.
According to a flight plan ABC said it had seen, the jet was registered as departing from Paris to avoid arousing suspicion.
In fact, it took off from Paris on Sunday before making a stop in Vigo to pick up Juan Carlos. The paper says he is now well shielded from paparazzi photographers in the luxurious Emirates Palace hotel, adding that high temperatures have so far kept him indoors.
But a manager at the hotel denied the former king was there, telling AFP: “We have no VIP guests.”
Juan Carlos has long had warm relations with the Gulf monarchies, and Spanish press reports say a transfer of $100 million to one of his Swiss bank accounts from late Saudi king Abdullah has come into investigators' sights.
After abdicating over corruption allegations stemming from public statements by a former mistress, Juan Carlos announced Monday that he was quitting Spain so as not to undermine his son King Felipe VI.