Simon & Garfunkel's last studio LP together was 1970's Bridge Over Troubled Water, which was released shortly after their split.
The duo most recently reunited at the 25th anniversary of the Rock And Roll Hall Of Fame concerts in New York in 2009.
Simon explained that the chance of a reunion is a "moot point" due to Garfunkel's throat problems.
When asked about a possible reunion, he told BBC Radio 4's Today programme: "[I] would just as soon not go back and visit the past."
A 13-date tour was planned back in 2010, but was later cancelled because of Garfunkel's voice issues.
However, Art Garfunkel said last year that his voice was "on the mend".
The 'Bright Eyes' singer stated in January that his relationship with Paul Simon was similar to a brotherly bond.
Watch Simon & Garfunkel perform 'The Sound of Silence' in 2009 below: