The Belgian winger intimated that he was considering his future at Stamford Bridge following the World Cup, but has hit top form under new manager Maurizio Sarri and co-leads the Premier League scoring charts with seven goals.
Real, meanwhile, sacked manager Julen Lopetegui and have endured a miserable start to the season, sitting in sixth place in La Liga.
And Thorgan, who plays in the Bundesliga with Borussia Monchengladbach, believes his older brother should think carefully about joining a club in such a state of flux.
Eden made the right decision to stay at Chelsea, he told Belgian newspaper HLN.
Chelsea werent keen on selling him and he had a strong start of the season.
Real are in a complex period. They sacked their manager, key players left. They have to rebuild.
He continued: I think Eden will see what happens at the end of the season. I know him. Hes not thinking about a move right now.
He will give everything for Chelsea. He doesnt want a clash with his club either. If he ever leaves, he will play it correctly.
More: Chelsea FC