Murray, who was released by the Titans in March, addressed both players when talking to ESPN's Adam Schefter recently.
"I think Derrick's a smart guy. He's a fast guy, very physical, athletic, and now that I'm not there I think he can hone in on being the guy," the 30-year-old Murray said, via Titans Wire. "And if they use him the right way and if he can consistently be the every down back, I think he has a great future, a bright future."
Titans offensive coordinator Matt LaFleur told reporters last month that the running game will remain the focal point of the offense with free-agent signee Dion Lewis joining incumbent starter Henry in the backfield.
Henry led Tennessee in rushing despite starting only two games during the regular season. He ran for 744 yards during the regular season and added 184 yards while starting both playoff games.
A second-round pick in 2016, the 6-foot-3, 247-pound Henry provides quite the contrast to the 5-8, 195-pound Lewis, who had a team-leading 896 yards and scored six touchdowns for the New England Patriots last season. Lewis also had 32 receptions.
Although Mariota is coming off his worst statistical season, Murray feels the future is bright for the former Heisman Trophy winner.
"I think he'll be great," Murray said. "Obviously he was a young guy when I was there, second and third year player, but he took strides every week, every year to better himself. He's a guy that works hard every single day he comes in. If he can be a little more vocal and really take charge of the offense I think he's gonna be great.
"A lot of guys in that locker room love him. They respect him. He works hard every single day putting in the hours, putting in the work. If he can really just be more vocal and take charge of that offense I think he's gonna be great."
Mariota completed 281 of 453 passes for 3,232 yards with 13 touchdowns and 15 interceptions in 15 games last season. The 24-year-old also rushed for 312 yards and five scores.
Murray is still looking for employment after reportedly visiting the Seattle Seahawks, Miami Dolphins and Detroit Lions following his release from the Titans.
Last season, Murray was limited to career lows in rushing yards (659) and yards per carry (3.6) while dealing with myriad injuries -- hamstring, knee and shoulder -- before a high ankle sprain in late December ended his campaign.
Murray rushed for a league-best 1,845 yards with the Dallas Cowboys in 2014, scoring 13 touchdowns on the ground.
A third-round draft pick of Dallas in 2011, Murray's production dipped to 702 yards on 193 carries with the Philadelphia Eagles in 2015 before rebounding to churn out 1,287 yards and nine rushing touchdowns with Tennessee in 2016.