Belgium international Courtois made the move to Madrid in 2018 and was joined at the Santiago Bernabeu by compatriot Hazard 12 months later.
Both players publicly flirted with the Spanish giants before making the switch and Courtois says he openly talked about playing for Madrid with Hazard.
"In the Chelsea dressing room, we spoke about the possibility of playing here," he told El Mundo.
"'The White House, the White House' we said. It was nice to speculate about it.
"Now, we are very eager to win trophies here."
Hazard has been limited to just 15 appearances for Madrid since arriving in a reported €100million deal due to injury and fitness problems.
The 29-year-old broke his ankle prior to the LaLiga campaign being suspended due to the coronavirus pandemic, but he has used the near-three-month hiatus as a chance to fully recover in time for the planned restart in mid-June.
"Hazard is back and with a lot of energy," Courtois added.
"The stoppage has enabled him to get fit again. He can help us win the title. He is a key player for us."
Real Madrid trail leaders Barcelona by two points with 11 games to play.