Rodriguez has fallen out of favour at Real Madrid since Zinedine Zidane took charge midway through last season.
The Colombia international has started just eight La Liga games this season, with Luka Modric, Casemiro and Toni Kroos ahead of him in the pecking order.
Liverpool favourites to sign Real Madrid's James Rodriguez
The Reds have been installed as 5/2 favourites to sign the 25-year-old as manager Jurgen Klopp looks to strengthen his squad.
James Rodriguez has struggled for game time under Zinedine Zidane
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A Ladbrokes spokesman said: “Don’t be surprised to see Rodriguez swap La Liga for Liverpool this summer, with Klopp keen to boost his ranks and the Colombian out-of-favour at the Bernabeu.”
The Mirror reported over the weekend that Liverpool are confident of landing the former Monaco midfielder, who Real value at £65million.