A fee has not been sorted yet between the two clubs, but a switch is edging closer.
Antonio Conte has targeted the right-back as competition for Victor Moses ahead of the new season.
Manchester City have been credited with interest in the Brazil international too.
However, Chelsea are leading the race for Danilo’s signature.
According to Brazilian outlet Globoesporte, the defender has reached an agreement with the Blues over his terms.
Danilo is keen to join Chelsea having struggled to settle at Real Madrid
Danilo has now left it up to Madrid and Chelsea to discuss his move
Danilo has now left it up to Madrid and Chelsea to discuss his move, with negotiations advanced.
Express Sport understands Danilo could cost as much as £35m to sign.
He is keen to join Conte’s side, though, as the 26-year-old believes he will get more game time at Chelsea opposed to Madrid.
The former Porto man has struggled to nail down a regular role in Zinedine Zidane’s team over the past two years.
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And Globoesporte now say Danilo will swap Madrid for Chelsea soon.
Conte has largely been left frustrated with the Blues’ transfer activity so far this summer.
A deal for Juventus full-back Alex Sandro has not progressed, and Chelsea also missed out on Romelu Lukaku to Manchester United.
But with Tiemoue Bakayoko now signed and Chelsea closing in on Danilo, it will help settle matters in west London.