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.
“David De Gea is Real Madrid’s No.1 transfer target”
“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.”