The Colombian playmaker has been heavily touted with a move to the Premier League over the past six months after falling out of favour at Champions League winners Real Madrid.
Manager Zinedine Zidane signalled that Rodriguez has no future at The Bernabeu after the French coach left the South American out of his squad for their 4-1 win against Serie A giants Juventus in the Champions League final.
Manchester United were thought to be on the brink of signing the 25-year-old playmaker as Jose Mourinho looks to prepare for a return to the Champions League next term.
Arsenal have been suggested as another potential destination for the South American midfielder this summer.
However, Chelsea are also interested in the former Monaco man considering the future of current midfielders Nemanja Matic and Cesc Fabregas remains uncertain.
Speaking to ESPN FC, football insider Moreno believes Rodriguez is most likely to be at Chelsea next term.
“I’d say Chelsea [are the club most likely to sign Rodriguez]. There are too many ‘James Rodriguezs’ at Arsenal,” Moreno said.
“The same questions you have about Ozil, you might have about Rodriguez.”
Chelsea won the Premier League title with a seven-point cushion over Tottenham Hotspur last term.
However, the Blues lost 2-1 to bitter rivals Arsenal in the FA Cup final at Wembley last month.
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