Dennison joined Buffalo shortly after Sean McDermott was hired as the team's head coach a year ago.
The move comes five days after Buffalo was ousted in its first playoff appearance in 17 seasons, via a 10-3 loss at Jacksonville in the wild-card round. But McCoy took the Green Bay Packers' offensive coordinator job and was sacked midseason.
Shula was on staff with McDermott in Carolina for six years, so there's an obvious connection there.
Other possible candidates include former Seattles Seahawks offensive coordinator Darrell Bevell, former New York Giants head coach Ben McAdoo, former Indianapolis Colts offensive coordinator Rob Cudzinski.
"We're not satisfied with the whole offense, and it wasn't just about [quarterback] Tyrod [Taylor]", Bulls GM Brandon Beane said Tuesday, per ESPN. "We felt like it was important for us to address our players and say, 'Listen, let's not beat ourselves.' And so we talked a lot during the week about poise".
Under Dennison's watch, the Bills took a big step back with the same quarterback, running back, and most of the offensive line still in place.
The offensive performance against the Jaguars was emblematic of the Bills' season, marked by negligible production and questionable play-calling. McDermott said the team had not heard anything new from the league since their last comments on the matter.
Dennison served as offensive coordinator with the Denver Broncos (2006-08, 2015-16) and with the Houston Texans (2010-13).
The decision to part ways with Dennison also raised questions about the future of Taylor, who has one year left on his contract.
The quarterback change backfired after Peterman threw five interceptions in the first half of a 54-24 loss.