Quinn really wanted to work with George Paton (now Broncos GM) when he went to Atlanta but it didn't work out. I'm not sure what the tie is but I wouldn't be surprised if there was already an under the table deal in place given their history, which may have been why he turned down the Jags.
With that said, getting rid of a defensive-minded HC who was generally regarded as one of the best DC's in the league before getting to Denver, and who mostly had really solid defenses while in Denver, in order to hire another defensive-minded HC who may be better off as a DC than HC just like the guy they just fired, well...might be a tough sell.
They'd be better off poaching Bienimy from the Chiefs and weakening their rival at the same time.