The enquiry was made as the Gunners were seeking a replacement for former manager Unai Emery and before the hiring of Mikel Arteta.
Bayat told HLN: “Arsenal has knocked on the door."
Bayat acknowledges they cannot compete with European heavyweights in terms of contract offers.
“We are not going to spend money that is impossible to spend. That would not be wise, but the pennies are certainly not all-determining," he added.