The Spanish international's signing has fuelled speculation that Mikel could leave the club in order to increase his chances of playing first-team football next season.
However, the Nigeria international told Goal.com: "I don't have a problem with the signing of Cesc Fabregas. We have played against each other a lot of times. We don't play in the same position anyway.
"Chelsea are my home away from home, my second home. You never know what's going to happen in football, but I'm very happy at Chelsea and I want to remain at Chelsea.
"I still have three years left on my contract and want to stay there. I want to congratulate Cesc with his transfer and I'm looking forward to playing with him."
Mikel has spent the last eight years at Chelsea.