The officer is accused of using a number of offensive terms in text messages, which have been reported to both Lancashire Police and the Independent Office for Police Conduct.
The force said it is investigating allegations made anonymously against an officer, who has been removed from front-line policing and placed on "alternative duties" until its enquiries are completed.
Messages allegedly sent by the officer included offensive terms for people of Asian backgrounds and gay men.
The IOPC - which oversees the police complaints system in England and Wales - said it is aware of a complaint against the officer and has asked Lancashire Police to investigate.
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A police spokesman said: "We have received an anonymous report alleging that inappropriate text messages had been sent by an officer.
"We are looking into those matters and the officer is currently on alternative duties.
"Due to the nature of the allegation the matter was referred to the IOPC who determined that a local investigation should be carried out."
Lancashire Police has not said which division the officer was working for when the allegations were made.