The Germany international had been expected to depart the Gunners, but no move materialised before the transfer window slammed shut on Monday evening.
And Podolski confirmed that he did not receive any concrete offers, despite several clubs enquiring about his availability.
“A move away from Arsenal did not fall through because I had no offers to move,” he told German publication Bild.
“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.”
Following a serious injury to striker Olivier Giroud, Arsenal boss Arsene Wenger insisted that Podolski would not be sold.
And the 29-year-old is happy to have the trust of the French manager after a candid conversation with Wenger.
“I had a very good conversation with the manager,” Podolski added. “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.”