After a frustrating and quiet start to the summer window, the Premier League champions are beginning to make progress with a number of signings.
The Blues completed a £34million move for Germany international Antonio Rudiger last week and are expected to unveil Tiemoue Bakayoko in the next few days.
Antonio Conte wants to bolster his squad at Stamford Bridge with two or three more additions and has identified Danilo as a prime target.
The 25-year-old only featured in 17 league games for Real last season and is said to be open to the idea of a switch to England.
According to Spanish outlet Marca, Chelsea are now closing in on securing a deal for Danilo but have yet to reach an agreement with the La Liga giants.
Antonio Conte wants to bolster his squad at Stamford Bridge (Picture: Getty)
Danilo endured a frustrating season and could be open to a move (Picture: Getty)
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Real are holding out for an offer of around £31million but Chelsea are understood to be waiting to see if the valuation will be lowered.
Danilo was said to be considering his future in the Spanish capital following the end of the season with his eyes on the 2018 World Cup and a place in the Brazil squad.