The Bundesliga side agreed a fee believed to be in the region of £3m for Bendnter last week, with the Gunners keen to offload the Danish striker.
After conducting contract negotiations this week, Frankfurt sporting director Bruno Hubner has confirmed that a deal has failed to materialise.
He told the club's official website: "We would like to thank Arsenal manager Arsene Wenger for the constructive conversations and the high level of cooperation.
"There was interest from all three parts, but in the end it did not match up."
Wage demands are thought to the reason behind a breakdown in talks, which sends Bendtner back to the drawing board in his search for a new club.
The 25-year-old has less than 12 months left on his contract at the Emirates Stadium.