Bruno Fernandes was reportedly angry with Mason Greenwood's lethargic attitude in training last week.
Manchester United maintain that Greenwood was off the pace - an subsequently left out of the Red Devils' 3-1 win over Everton - because he was suffering with illness.
But regardless of whether Fernandes was in the right to voice frustration at his team-mate, Solskjaer won't be concerned about a problem behind the scenes.
The Norwegian has previously spoken out about what Fernandes is like, and is a huge fan of the fact that the Portuguese is competitive.
After Fernandes put his finger to his lips when arguing with Manchester City boss Pep Guardiola, Solskjaer said: "The whole club [has been lifted by Fernandes' arrival]. Because he has everything I spoke about.
"He works hard, he is humble enough, he's got the desire and commitment, but he's also got the X-factor. He is a risk-taker, he's got the courage to make mistakes and if you make enough mistakes it'll be corrected into fantastic assists or goals.
"You need a character here, you need character at this club, but this team they have got that. They have learned through some hard times this season, because we have been a young team and we have started something we believe in and Bruno has helped that."
Manchester United have been lacking character in recent weeks, suffering back to back defeats at home to Arsenal and then in the Champions League.
But last time out the Red Devils beat Everton 3-1 to get their season back on track and cool speculation that Mauricio Pochettino is ready to replace Solskjaer at the helm.
Will Man United finish in the top four this season? Have your say here.
* Sign up to the Mirror Football email here for the latest news and transfer gossip
