The Chelsea goalkeeper is a long-term target for the Spanish giants.
Real president Florentino Perez is keen to replace Keylor Navas at the Bernabeu.
Courtois, Manchester United No 1 David De Gea and Roma’s Alisson have all been tipped to replace Navas this summer.
And according to the bookies, Courtois is off to Real in the coming weeks, with the move priced at 10/11 – shorter than they’ve ever been.
Alex Apati of Ladbrokes said: “It’s all change at Chelsea this summer and the latest odds suggest Courtois is set for a return to the Spanish capital.”
Atletico Madrid are next in line to land the Chelsea ace, priced at 6/1, while PSG are also in the running at 16/1.
Chelsea are readying a summer shake-up, with former Napoli boss Maurizio Sarri expected to replace Antonio Conte at Stamford Bridge in the coming days.
Express Sport understands Sarri has a £140m transfer wish list for when he takes over at Chelsea this summer.
Sarri wants Napoli right-back Elseid Hysaj and forward Dries Mertens, Juventus centre-back Daniele Rugani, Inter Milan’s Uruguayan midfielder Matias Vecino and Nice midfielder Jean Seri.
The incoming Blues boss will also be desperate to keep hold of Eden Hazard.