Mertesacker was one of several players to move to the Emirates towards the end of the transfer window but, with a number of the club's key players having left or currently unavailable through injury, progress has been slow.
The Gunners have taken just seven points from their opening seven games and, after Sunday's defeat at Tottenham, sit 15th in the table, but Mertesacker has no doubts about the manager or the direction of the club.
"The coach has been the pride of Arsenal for years," he said in an interview for the German Football Association website. "Arsene Wenger does not sign players about whom he is not totally convinced. He gives this feeling to everyone on a daily basis. This knowledge gives me a lot of security.
"He has a huge reputation there and enjoys complete confidence. For the Arsenal fans, Wenger is a hero and he cannot lose this status. There is no one here who is not certain that the success will return. We have a talented team with a lot of potential lying dormant within us and it's only a matter of time before that comes to the surface."
With the sweeping changes to the side, it was always likely that Arsenal would need time to gel, and Mertesacker says he is still struggling to adjust to life in London.
"I've only been gone a month from Germany," he said. "I have not yet properly acclimatised. Sometimes it feels like an extended holiday. Only slowly am I starting to get used to the fact that the centre of my life is now actually in London.
"I have been living in England since the middle of September, but it doesn't yet feel like home. I don't have my own house or my own flat. There is a lack of anchor points which I already had in Germany, but that takes time, it's normal.
"We have many new players, but I feel that we have integrated very quickly. I still have communication problems, but given the circumstances this is inevitable."
He added: "Arsenal is one of the top teams in the world and the level of the league in general is very high, but it is clear that mistakes happen. They are almost inevitable in a team which has not yet gelled."