Antonio Conte helped the Blues win the Premier League in his debut season. The ex-Juventus and Italy coach wants the west London club to bolster the squad as they return to the Champions League after a year's absence.
According to the Spanish publication AS, Conte identified Rodriguez and his club teammate Alvaro Morata as summer transfer targets. However, the striker is edging closer towards completing a move to Manchester United after agreeing terms "very quickly" with Jose Mourinho's side.
Rodriguez was wanted by the Italian manager in the January transfer window as a replacement for Oscar. The Brazilian left Chelsea and completed a switch to Chinese outfit Shanghai SIPG during the mid-season.
The Colombian international decided against completing the transfer. He wanted to continue at Real and win his place back in the starting lineup. However, things did not go as per his plans and the Champions League and the La Liga winners are looking to offload him and Morata this summer.
Chelsea are not the only club interested in signing Rodriguez. Another Spanish publication earlier reported that the Blues' league rivals United and Arsene Wenger's Arsenal are also in for his signature. Spanish television programme El Chiringuito revealed that Real have turned down the Gunners' approach for the 25-year-old.
In addition to this, Paris Saint-Germain, Juventus and Bayern Munich are reported to be interested in Rodriguez. However, AS suggests that Chelsea are leading the race in securing his services and the player is edging closer towards completing a switch to the English capital.
Conte is looking to offload star striker Diego Costa and his compatriot Cesc Fabregas. The Brazil-born Spain international has publicly revealed that his manager no longer requires his services at the club.
The funds from the potential sale of Rodriguez and Morata are likely to help Real in their ongoing pursuit of AS Monaco's Kylian Mbappe. The France international is a target for a host of European clubs, including the Spanish capital club.
Rodriguez has scored 11 goals and registered 11 assists across all competitions for Zinedine Zidane's side last season.