Cillessen joined Barcelona last summer after Claudio Bravo left the Nou Camp for Manchester City.
But with Marc-Andre ter Stegen as the number one goalkeeper, Cillessen has found it tough to play regularly.
The Holland international made just nine appearances in all competitions, with only one coming in La Liga.
Cillessen signed a five-year deal when he arrived but has already begun thinking about his future.
Barcelona line-up next season with Ander Herrera Thu, May 25, 2017
Click to reveal a possible Barcelona line-up for next season if they sign Ander Herrera
Play slideshow Getty Images 1 of 11
GK: Marc-Andre ter Stegen
If I play very little, we will see in the winter transfer window
"I have not thought about listening to offers, I'm fine here," the 28-year-old told Spanish newspaper Sport.
"If I play very little, we will see in the winter transfer window, but for the moment I am not thinking about anything.
"I'm not happy if I don't play. When I arrived I knew that I would have to adapt myself to many new things."
Jasper Cillessen is considering his Barcelona future
Get Quotes on Home Insurance
Despite his first-team woes, Cillessen believes he is good to supplant Ter Stegen as Barca's number one keeper.
He added: "Next season without a doubt I will fight to be the number one goalkeeper at Barcelona.
"Of course I feel capable. If I wasn't, Barcelona wouldn't have signed me.
"They signed me because they think I have the potential necessary to play here, not to be on the bench."