Undefeated Rams in the market for a productive edge rusher

The Rams are 8-0 and a favorite to play in the Super Bowl, but with Tuesday’s NFL trade deadline looming they still might be in the market for a missing piece.

The most pressing need is for a productive edge rusher, and coach Sean McVay said Monday that general manager Les Snead was exploring possibilities.

“That’s the main one,” McVay said during a news conference in Thousand Oaks.

The Rams rank eighth in the NFL with 22 sacks, but tackle Aaron Donald has 10 of them.

Second-year pro Samson Ebukam and veteran Matt Longacre have two and zero sacks, respectively. Rookie lineman John Franklin-Myers also has been deployed from the outside linebacker position and has one sack.

Denver Broncos end Shane Ray has surfaced in several media reports as a possible trade target for the Rams because of his connection to defensive coordinator Wade Phillips, who coached him in 2015 and 2016. But that also might be the result of Broncos general manager John Elway baiting the hook as opposed to genuine interest from the Rams.

After the 2017 season, the Rams moved to overhaul the defense to better fit Phillips’ 3-4 scheme. They traded linebacker Robert Quinn and did not bring back linebacker Connor Barwin, two veterans who combined for 13½ sacks.

The Rams’ rush presence from outside linebackers was regarded as a question mark throughout training camp and the preseason.

In August, the Rams brought in former New Orleans Saints and Washington Redskins linebacker Junior Galette for an interview and physical, but they did not put him through a workout.

The Rams converted lineman Dominique Easley to outside linebacker, and he played well in rotation with Longacre before suffering a season-ending knee injury in Week 3 against the Chargers.

The Rams have until next week to decide whether to activate rookie linebacker Ogbonnia Okoronkwo, who was sidelined during offseason workouts and training camp while recovering from foot surgery. Okoronkwo has been practicing, but he has mainly been utilized as a scout team player for the first-team offense to work against, McVay said.

McVay indicated that the Rams are exploring adding to other unspecified position groups as well.

“If it’s something that fits, then that’s something that we’ll do,” he said.

Looking for the next McVay

In the aftermath of the Cleveland Browns’ firing of coach Hue Jackson and offensive coordinator Todd Haley, members of McVay’s staff have been mentioned as possible candidates to fill the vacancies.

Quarterbacks coach Zac Taylor and passing game coordinator Shane Waldron are regarded as hot prospects.

Both are “great communicators, great teachers, great leaders,” McVay said.

“Would I be upset if we lost them? Would I be very stressed out?” he said. “The answer is yes, I would.”

Browns owner Jimmy Haslam told Cleveland reporters during a news conference that the team had not yet considered who it might hire for a team that features quarterback Baker Mayfield, the No. 1 pick in the 2018 draft.

“We really have not focused on that,” Haslam said. “We are focused on making these changes and putting the team in the best position to winning the last eight games.”

Because of McVay’s success with quarterback Jared Goff, the Rams’ model of matching a young offense-minded coach with a young quarterback could become an NFL trend.

The Chicago Bears attempted to duplicate the Rams’ formula by hiring Matt Nagy for a team with quarterback Mitch Trubisky.

After last season, the Tennessee Titans interviewed Rams offensive coordinator Matt LaFleur to become their head coach. They ultimately hired him to call plays as offensive coordinator, responsibilities he did not have under McVay.

The Oakland Raiders hired veteran Rams quarterbacks coach Greg Olson as offensive coordinator.

The Browns are not expected to hire a coach until after the college or NFL regular seasons. Chatter about Taylor and Waldron will not be a distraction, McVay said.

“These guys have the right mind-set,” he said, adding, “They’ll continue to work exactly like they have, doing an excellent job coaching and being the best Rams coaches they can be.

“Down the line, I think they know that if you want to continue to be in those conversations, if that’s something that they have goals to be able to try to achieve, then we’ve got to continue to have success as a team.”

McVay, who is expected to receive an extension from the Rams after this season, also addressed speculation caused by an oddsmaker’s internet post that he might be a candidate to coach the Browns.

“I couldn’t be happier to be here with our players, with this organization, working for a great owner in Mr. [Stan] Kroenke,” McVay said. “Unless they decide they want to make a change I wouldn’t want to be anywhere else.”

Etc.

Receiver Cooper Kupp has “a very good chance” of returning from a knee injury and playing against the New Orleans Saints on Sunday, McVay said…. The Rams are off Tuesday. They resume practice Wednesday.

gary.klein@latimes.com

Follow Gary Klein on Twitter @latimesklein