The People reports that Inter and Real believe they can persuade Suarez to leave Liverpool following the controversy surrounding the Uruguayan’s eight-match ban for racially abusing Manchester United star Patrice Evra.
Suarez has been a hit at Liverpool since joining the club in a £25million deal from Ajax last year.
Suarez’s agent is Pere Guardiola, brother of Pep, boss of Real Madrid’s rivals Barcelona. That could prove a major stumbling block in Real’s move to sign the striker.