The Manchester United star has been heavily linked with a move to the La Liga giants in recent months.
De Gea, 26, nearly joined Real in 2015 but a late fax ended any hope of a move.
And BetStars reckon Zinedine Zidane has made De Gea his priority target this summer, with the Spain international priced at 6/4 to join Real.
BetStars spokesperson Ian Marmion said: “Real Madrid have made signing Manchester United goalkeeper David De Gea their number one priority and have been priced at 6/4 to acquire the Spanish shot stopper.
“The long-term target for the Galacticos is keen on a move back to his homeland and Los Blancos are keen to replace the inconsistent Keylor Navas.
“The second favourite to sign for Real is PSG right-back Thomas Meunier.
“The 25-year-old defender has been linked with a move away from the Parc des Princes after the French side signed Dani Alves from Barcelona.
“The Belgian has been priced at 5/2 with BetStars to make the move to the Bernabeu.
“Tottenham star Dele Alli has also been linked with a move to Real Madrid with the Spanish side keen to add more creative midfielders to their ranks.
“Interest in the English 21-year-old has waned in recent weeks, with the Spurs star now priced at 6/1 to swap north London for Madrid.
“After Real made De Gea their primary target, their interest in Pierre-Emerick Aubameyang has declined and the Gabonese striker is now available at 8/1 to become a Galactico.
“Odds on Eden Hazard and Kylian Mbappe joining Real Madrid have also drifted with them both being priced at 10/1 apiece.”