Solskjaer is feeling the heat as Manchester United boss after suffering a woeful finish to the Premier League season.
United won two of their last 10 games following Solskjaer’s permanent appointment and failed to secure a top four finish and Champions League qualification.
The Norwegian is set to oversee a huge overhaul of his squad this summer.
Several big names are expected to leave Old Trafford, but Rooney believes the issues run deeper than this.
The United legend, who is the club’s greatest ever goalscorer, believes Solskjaer needs to strike the balance between fear and respect to get the best out of certain individuals that have been missing this season.
The former England captain said: “It’s a tough one because to watch Manchester United struggle is always tough.
“When Ole came in, he did a fantastic job and you could see the players were given that bit of freedom and you could see they loved it and they earned the right to win game with how they were playing.
“But then all of a sudden, I don’t know whether it’s players being linked to other teams or players down tooling.
“They need to fear Ole Gunnar, they need to fear Michael Carrick – they need to respect them but fear them also”
“I don’t think it is that but for some reason they just didn’t perform the last seven, eight games of the season, which has cost them.
“I think the players need to fear someone.
“They need to fear Ole Gunnar, they need to fear Michael Carrick – they need to respect them but fear them also.”
Rooney, who plundered 253 goals in 559 appearances during a glittering career with United, believes some of the current crop need to be more focused and get their priorities in order.
He added: “The way the game has gone has changed; the society has changed.
“You’ve got social media. You’ve got players losing a game and then posting something on social media about their new clothing range or aftershave, whatever, they are bringing out, which I find remarkable.
“So, when fans speak up on it and say, ‘why are you posting that?’ they always have the marketing people to blame.
“Take responsibility. They work for you. Them marketing people work for you.
“I have people who do similar stuff for me and they would never do anything without my instructions.
“If that’s what you’re doing, you’re sitting at the top of that business, you have to take responsibility for that.
“These players almost like to find someone to hide behind, whether that’s on the social media or on the pitch – and that’s what they’re doing.”