The 24-year-old Ghana international arrived at Wanda Metropolitano in 2011 and signed a contract extension for another five years, which keeps him at the club until 2023.
"All matches are equally as challenging for us," Partey was quoted as saying by Marca.
"We're ready to compete [Barcelona]. We have to be strong and fight for each ball as if it were the last," he added.
Partey also showered praise on teammate Antoine Griezmann who has been brilliant of late, scoring four times in their last outing against Leganes.
"[Griezmann]'s always working hard, sometimes he just lacked luck," Partey said. "He's at his natural level, it's normal that in some games he doesn't score.
"He works hard and deserves the good things that happen to him," he added.
Partey has made 82 appearances and scored nine goals for the club since making his debut against Espanyol in November 2015.