The German international signed for Arsene Wenger’s side on transfer deadline day and admits he has found it difficult to adapt to England.
However, he is confident that with time and further training he will adapt to life in London.
He told reporters: “I still have communication problems, but given the circumstances this was unavoidable. Due to the lateness of the transfer, I could do very little to prepare myself.
“I've only been gone from Germany for a month. I have not yet entirely acclimated. Sometimes it feels like an extended vacation. I'm slowly starting to get used to the fact that the centre of my life is now actually in London.
“I have called England my home since mid-September, but it still does not feel like home. I still have no house, no apartment of my own. There is a lack of anchor points, which I had had in Germany. But it takes time, that's normal.
“I feel in good hands there [at Arsenal], the atmosphere is very pleasant, very casual. We have many new players, but I think we have adjusted to one another very quickly."
Mertesacker believes the faith shown in him and his team-mates by manager Arsene Wenger gives them the confidence to bounce back from a disappointing start to the season that sees them in 15th place in the Premier League after seven games.
He said: “The coach selects no players with whom he is not absolutely convinced. This feeling he conveys to me even in our daily work. This knowledge gives me and the players a lot of security.”
The 27-year-old also revealed he has an affinity with Arsenal stretching back 15 years after buying a Gunners shirt.
"Yes, it began in 1995. As a football-mad family, every child was allowed to choose a shirt in a store," he added.
"My brother chose a Manchester United shirt; myself, Arsenal. From then on I had a relationship with this club."