The Arsenal striker was expected to complete the transfer on Tuesday when he arrived in Germany to finalise the deal.
However, Frankfurt chairman Heribert Bruchhagen says a move for the Denmark international is not realistic, with talks rumoured to have broken down due to Bendtner's wage demands.
Bruchhagen said: "After weighing up all the arguments, Bendtner turned out not to be a realistic prospect.
"Now it's up to us. There are no problems with Arsenal. We have to see if it's financially viable."
Bendtner spent last season on loan at Serie A champions Juventus but they opted not to make the deal permanent after he failed to score a goal.