The 19-year-old is on loan from the Premier League giants until January and has impressed so far for the Cumbrians.
The former Leeds youngster remains well down the pecking order at Stamford Bridge and has hinted he would be interested in joining the League One side permanently.
"I'm just trying to impress as many people as possible really and improve my reputation," he told skysports.com.
"I'd like to get as many games under my belt as possible and hopefully a few goals along the way and we'll see what happens from there.
"League One football isn't a step down really in my eyes because it is a new challenge for me, with some tough games technically at this level and it can only help me develop as a player."
The youngster made a handful of appearances for League Two outfit Port Vale last season and he is enjoying another chance to impress at first-team level with Carlisle.
"It has been going really well so far this season for both me and the club because we've been playing well and I've been getting games under my belt, which was my aim when I joined on loan at the start of the season," he concluded.