Citing two sources it did not name, the publication said Incognito and at least one other Dolphins player denigrated the team employee's ethnic background "in view of other team staff members."
The sources said Dolphins team officials were aware of the alleged abusive behavior but allowed it to continue.
Incognito "would sometimes dress in garb from the staff member's culture and then make profane jokes about that culture" and joked that the man's wife "had sexual relationships with several members of the team," the report said.
Incognito was suspended indefinitely this month amid allegations he bullied teammate Jonathan Martin.
ESPN, also citing sources it did not name, reported the Dolphins are aware of the latest allegations against Incognito, whom Martin has accused of using racial slurs and threatening violence against him and his mother.
Martin left the team Oct. 30 and the Dolphins have suspended Incognito.
NFL investigator Ted Wells is in Miami this week conducting a probe of the allegations.