Reports have recently linked Kolarov with a £15million move to Premier League side Manchester City.
“I hope for the best,” said the 24-year-old. “Recently, the (Lazio) club president, Claudio Lotito, promised me that he would let me leave for Real Madrid.”
Real Madrid boss Jose Mourinho tried to sign the defender while in charge at Inter Milan.
“I hope that this second time works out,” said the defender. “A few things have to still fall into place to complete the puzzle, but things are on a good path.
“Real are one of the greatest clubs on the planet and wearing that shirt is an honour for anyone who dedicates himself to football.”