"I am capable of doing this job and I will prove it in the future. I have no doubt about that," Caro told Spanish sports daily AS on Saturday.
Caro took over Real after the club sacked Wanderley Luxemburgo in December where he lead the team to a series of successes before crashing out of the UEFA Champions League and falling behind rivals Barcelona in their local campaign.
"I still haven't given up hope that I can continue coaching Real Madrid. That's my dream," Caro insisted.
The Spanish giants have insisted that the 48-year-old was expected to remain in his position as team coach until the end of the season before signing a new high-profile successor with the likes of Rafael Benitez, Fabio Capello and Carlo Ancelotti already linked with a move to the club.