"Nicolas is smiling all the time because he feels very comfortable at Chelsea and this is exactly what he has been waiting for," a friend told the Daily Mail.
"This is the best time in his career. He is playing regularly at the top level and with great consistency. He has been a star from very early on and maybe he wasn't ready but now he is. He has got everything now.
"Playing Liverpool will be a big a game for him but no more than for anyone else because he has played against them for other clubs since his time there."
Anelka has faced Rafael Benitez's side at Anfield already this season with Bolton in a 4-0 defeat in December. His former club opened preliminary talks with Chelsea soon after and the £15million deal went through last month.
Negotiations went relatively smoothly but Anelka's settling in period at the Bridge has been significantly less bumpy. The 28-year-old has slotted straight in from his first substitute appearance.
He said: "Everybody speaks to me as if I've already been here a long time. It is strange as it is like I am in another world. I was fighting against relegation at Bolton and now I am fighting to win something."