The Kop kings have already inquired about the Mali-born
25-year-old who spent five seasons in France with Lyon before
signing for Real 18 months ago.
But Liverpool face competition for Diarra from other clubs.
His agent Federico Guerra said: "Inter Milan contacted me in
January to try to sign Mahamadou in the last transfer window.
"We were also contacted by Liverpool, AC Milan and Juventus.
Diarra still has three years left on his contract but we're willing
to listen to all the offers and then we will talk to Real to see
what is decided."
Liverpool are also chasing Schalke04's £5million-rated Rafinha,
22, who was named best full-back in the 2005 Under-20 World
Cup.
Kop scouts have watched the right-back in the Bundesliga and
were disappointed he was left out of Brazil's team for the recent
friendly against the Republic of Ireland in Dublin.
Rafinha said: "I am very happy that clubs from both England and
Spain are watching me."