The Argentine goalkeeper was not happy at the lack of playing time on offer at the Gunners.
"I was desperate to leave in January," Martinez said in an interview with Goal.com.
"Even if he [Emery] didn't want it.
"I had Reading and other clubs after me - both abroad and in England, but my first option was Reading because I knew the league, I knew the manager [Jose Gomes] and his style, so I had no doubts about coming.
"I liked the challenge. They were in the bottom three, so it was a massive challenge which could go either way. I was comfortable at Arsenal, sitting on the bench or playing Europa League games - but for me that is not a challenge.