Frankfurt chairman Heribert Bruchhagen announced earlier on Thursday that a deal was in doubt.
The plug has now been pulled, despite a fee having been agreed with Arsenal.
Bendtner was open to the idea of moving to Germany, after being deemed surplus to requirements at Emirates Stadium, but his wage demands have proved to be a sticking point.
Frankfurt are now believed to have turned their attention to Sparta Prague's Czech Republic international Vaclav Kadlec.
On the breakdown in discussions with Bendtner, sporting director Bruno Hubner 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."
Bendtner is still expected to be on the move this summer, but has one year remaining on his contract at Arsenal if now agreement is reached.