The Portuguese defender and the Argentine midfielder have been deemed surplus to requirements at the Santiago Bernabeu, and they look set to leave the club sooner than later
The duo are not part of coach Jose Mourinho's plans for the new season and have been given permission to discuss their future with any interested clubs, according to AS.
Carvalho, 34, signed for Los Blancos in 2010 after previously working with Mourinho at Porto and Chelsea, but endured a frustrating 2011-12 season as he made just 13 competitive appearances.
As for Gago, the Argentine midfielder returned to the Spanish champions at the end of the season following a loan spell at Roma as the new Giallorossi coach Zdenek Zeman decided against signing the 26-year-old.
Kaka, Angel Di Maria and Gonzalo Higuain were among the 22 players who took part in the morning session.
Madrid's first Primera Division match of the new season is scheduled for August 18, against Valencia.