The Blues parted company with the veteran holding midfielder last week, allowing the Frenchman to join Paris Saint Germain.
"I played that role sometimes last season and hopefully I'll have a long run in the team now," said Mikel.
"It's something I've wanted - a run in the team - and I suppose Claude's departure has opened up that door for me, but I was playing in that role when I was in the team last season too.
"I was in and out of the team last season, but when I was given a chance under (former manager Jose) Mourinho before, I actually did okay in that holding role. I think I did very well under Mourinho and was playing regularly.
"Of course, when a new manager comes in everyone has to start afresh and roll up their sleeves. In Avram Grant's time I was in and out of the side, and that was a bit frustrating, but it's what happens in football.
"This time, under the new boss, I will try to make it my position in the team each week."