United have asked for help from the Championship club as they seek to gather more information about the incident which occurred outside Pride Park on Thursday night.
- Dawson: FA Cup run reflects well on Solskjaer
Ole Gunnar Solskjaer's team booked their place in the quarterfinals of the FA Cup with a 3-0 win over Derby.
After the game, a video on social media showed fans subjecting Lingard to a torrent of foul-mouthed abuse as he got on the bus alongside his teammates.
United have condemned the incident and are offering support to Lingard.
Lingard, 27, played the full 90 minutes against Derby but has not been part of Solskjaer's starting lineup in the league since New Year's Day against Arsenal, and has scored twice across all competitions this season.
United are unbeaten in their nine matches, heading into Sunday's derby against Manchester City, where visiting boss Pep Guardiola said he hopes to welcome back midfielder Kevin De Bruyne to his starting lineup.
"He's getting better," Guardiola told a news conference on Friday, when asked about the Belgium international, who missed the midweek FA Cup fifth-round win over Sheffield Wednesday.
"He will improve, he feels better. He's not perfect, so we'll see."