Fred was at fault for Leicester's opening goal during the 3-1 defeat at the King Power Stadium. After the game, a number of racist messages were left on the Brazil international's Instagram account, some including a derogatory emoji.
Speaking after the final whistle, manager Ole Gunnar Solskjaer refused to blame any of his players for the result and instead said his team lacked "spark."
"When we win, we win together, and when we lose, we lose together," he said. "We're not pointing fingers and blaming."
Fred and teammate Jesse Lingard were also racially abused during a 2-1 win at Manchester City in December 2019. United have previously released statements condemning the abuse directed at their players and branded those responsible as "mindless idiots."
Sources have told ESPN the club remain keen for social media companies to assume the lead in helping to protect their players, including taking steps to ensure accounts are verified rather than anonymous.