The Germany international was heavily linked with a move away from Emirates Stadium and he was made aware of enquiries from several clubs.
However, he had no interest in returning to the Bundesliga if he could not join home-town club Cologne, and is now focused on his future at Arsenal following productive talks with Wenger.
The Gunners manager has made it clear that Podolski remains an important of his plans and the 29-year-old insists he has no worries about the competition for places.
Having been given an extended break after the World Cup, Podolski made his first appearance of the season as a substitute against Leicester City on Sunday and is looking to make a big contribution as soon as he returns to full sharpness.
He told BILD: “A move away from Arsenal did not fall through because I had no offers to move.
“There have been enquiries from other countries, also from Bundesliga clubs, but I am from Cologne and it would have been tough for me to represent any other German club."
Speaking about Wenger, Podolski added: "I had a very good conversation with the manager. He has stressed he is putting trust in me and my qualities.
“I do not have to fear anyone at Arsenal. I am just back in training for two and a half weeks.
“If I am at 100 per cent fitness, I do not fear any competition for places in the first XI."