Courtois has been linked with a switch to the Bernabeu since last season, and Marca reported that Real could make a move if they failed to acquire Manchester United’s David De Gea.
Fabregas told Cadena Cope radio: “It wouldn’t surprise me at all because Courtois is the best goalkeeper in the world.
“It’s normal that the best teams in the world want the best goalkeeper in the world.”
Belgium international Courtois, who spent three years on loan at Atletico Madrid before replacing Petr Cech at Stamford Bridge, said earlier this season that he would like to return to Spain one day.
But Fabregas said: “Chelsea is a top club and, for the future of this team, Thibaut is a very, very important player.
“That is more so considering Chelsea’s future aspirations in terms of competing in the Champions League next season and winning the Premier League title.
“You need the best players to compete for the top trophies and Thibaut is one of them.”