Rubuta ci gaba don wannan sakin layi - Córdoba ya jagoranci Colombia don lashe gasar Copa América ta 2001, inda ya zira kwallaye daya a wasan karshe. Córdoba ya kuma buga wa kasarsa wasa a gasar cin kofin duniya ta 1998 (ya dauki lambar rigar lamba 2 daga Andrés Escobar wanda aka kashe a gasar da ta gabata) ba tare da ya bayyana a wasa ba, FIFA Confederations Cup ta 2003 (inda suka gama a matsayi na hudu), da kuma wasu bugu uku na Copa América (1997
, 1999 da kuma 2007).