Team spokesman Greg Bensel says the pair visited Saints headquarters Thursday.
Ramsey and McCown both began their NFL careers in 2002.
Ramsey is a Ruston, La., native who played for Tulane. He started 11 games for the Redskins in 2003, but has played in only four games since 2006 in stints with Denver, Tennessee and Detroit.
McCown started 13 games for Arizona in 2004. He spent the past two seasons as a backup in Carolina.