Salah has failed to start their last three matches and lashed out at the club and coach Arne Slot following Saturday's 3-3 Premier League draw with Leeds United, saying he had been made a scapegoat for their poor start to the season.
The Egyptian, who signed a two-year contract extension in April, has become an iconic figure in an eight-year spell at Liverpool in which he has won two Premier League titles and scored 250 goals in all competitions.
However, he has scored just five goals and appeared in 19 games in all competitions this season.
"He is absolutely destroying his legacy at Liverpool," Rooney said on his podcast. "It would be sad for him to throw it all away. He's gone about it all wrong.
"Arne Slot has to show his authority and pull him in and say, 'you are not travelling with the team, what you said is not acceptable.'
"Take yourself off to Afcon (Africa Cup of Nations) and let everything calm down. If I was him there would be no way he would be in the team."
Salah had said he felt as if he had been "thrown under the bus" with Liverpool failing to reproduce their title-winning form from last season.
They are ninth in the current campaign, 10 points behind leaders Arsenal after 15 games.
"If anything, he has thrown Liverpool under the bus with his words... ," Rooney said. "I am sure over the next couple of years he will regret saying what he has."