The Denmark forward appeared to be on the brink of a switch to the Commerzbank-Arena after Eintracht confirmed Bendtner was in Germany on Tuesday to finalise his transfer.
However, talks appear to have broken down, with the 25-year-old's wage demands a possible stumbling block.
Bruchhagen told kicker.de: "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.