Mike Mularkey has agreed to part ways with the Tennessee Titans, who announced Monday that the sides "couldn't come to an agreement over the future."

Titans controlling owner Amy Adams Strunk acknowledged in a statement that the organization had discussed a potential contract extension with Mularkey, who in 2017 coached Tennessee to its first postseason appearance since 2008.

But the talks revealed that Mularkey and the Titans "saw different paths to achieve greater success," according to Strunk.

Rams offensive coordinator Matt LaFleur is now set to interview for the Tennessee head-coaching job, a source told ESPN's Alden Gonzalez.

Titans general manager Jon Robinson addressed the decision to part ways with Mularkey during a news conference Monday.

"I just felt like we needed to go in a different direction, and maximize the skill sets of the players on the field," Robinson said. "I think in any organization, not to speak for other teams, but its ownership, the head coach and the general manager, they all have to be on the same page."

The Titans were open to extending Mularkey, whose contract ran through 2018, but they wanted to make changes to his coaching staff, sources told ESPN's Cameron Wolfe.

"It is certainly unfortunate that we couldn't find enough common ground," Strunk said. "I generally believe that continuity is the best path for success, but I also view this as an important moment for our football team as we try to make that next step to sustained success on the field. Jon will begin the search immediately to identify that person."

Mularkey, 56, went 20-21 in parts of three seasons with the Titans and guided Tennessee to back-to-back 9-7 records in his two years as the team's full-time coach.

The Titans ended an eight-year postseason drought and won a playoff game for the first time since 2003 with their 22-21 victory over the Kansas City Chiefs in the wild-card round earlier this month.

Mike Mularkey went 18-14 in his two full seasons as Tennessee's coach and helped guide the Titans to their first postseason victory since 2003. Jim Brown-USA TODAY Sports

But Tennessee was eliminated Saturday with a 35-14 loss to the New England Patriots.

"I want to thank Mike Mularkey for his contributions to our franchise over his tenure with our organization," Strunk said in Monday's statement. "He took over our team during a low moment and together with Jon built a solid foundation for our franchise. I appreciated that Mike devoted himself to this team and the community."

Strunk had publicly supported Mularkey just over a week ago, saying in a Jan. 7 statement that "to eliminate any distractions moving forward, Mike Mularkey is our head coach and will be our head coach moving forward."

That vote of confidence was prompted by widespread speculation about Mularkey's future -- a situation that Mularkey called "ridiculous" after Tennessee rallied from an 18-point deficit to beat Kansas City on Jan. 6.

Robinson said the team is searching for ways to get more out of the Tennessee offense, and that is a significant factor in why they parted ways with Mularkey.

Of the upcoming coaching search, Robinson said, "We're going into it with really no preconceived notions. We have a vision for what we want the next head coach to look like. We're looking forward to talking to candidates and seeing if they fit that bill.

"We've started that search this morning, going through names and bios, and starting to build a list of potential candidates. It certainly helps to have relationships in the league, and be able to call on those relationships that might have a connection with a potential candidate, even though I might not have a one-on-one relationship with that person. Someone you can trust that will shoot you straight on the candidate."

The Titans are the first NFL team in 15 years to change head coaches after a season in which they won a playoff game. The San Francisco 49ers fired Steve Mariucci in 2002 after they beat the New York Giants in the wild-card round and lost to the Tampa Bay Buccaneers the following week.

ESPN Stats & Information contributed to this report.