The pair previously collaborated on a live version of the Tears For Fears track in aid of Cyndi's charities, and were so pleased with the results they want to cut a studio version.
A source told website Music Daily News: ''Adam and Cyndi talked after their performance. They want to record their duet of 'Mad World' at the studio and release it. It's just a project they want to do for fun.''
The first time the pair performed the song together was at the 'Cyndi Lauper & Friends: Home for the Holidays' even in New York over Christmas.
Ahead of their collaboration, Adam said: ''I can't believe she asked me to do this! This is amazing.''
'Mad World' was originally a hit in 1982 for Tears for Fears, reaching number three in the UK singles chart. It also notably topped the UK singles charts in December 2003 when it was covered by singer Gary Jules.