The Spanish defender, who usually plays on the right of a back four, has deputised at left-back in the absence of Cole, and Mourinho said that the 24-year-old may continue in the position.
"Azpilicueta is playing very well," Mourinho told West London Sport after Chelsea's 2-2 draw with West Bromwich Albion.
"Let's see what happens next week, but he played well against Schalke and he played very well again with zero mistakes.
"I didn't like his (Cole's) performance against Newcastle so made a change and the answer from Azpi was good and I didn't feel I had any reason to leave him out."
Chelsea's next game sees them travel to West Ham United on November 24.