And according to the Daily Mirror, Cole, a free agent having been released by West Ham this summer, could be the Italian's first signing.
Ranieri worked with Cole in his time at Chelsea, giving the striker his debut in 2002 and praised him as being the best young player he had ever worked with at the time.
Aston Villa, Norwich and West Brom have all been linked with the former England striker with the latter trying to sign him In January - but the Hammers blocked Cole from leaving.
Cole started out at Chelsea where he found himself enjoying loan spells at Wolves, Charlton and Aston Villa before signing for West Ham in 2006.
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