Yesterday, at 4pm, the Good Morning Britain host tweeted about a incident in which a man called Kane Finch had posed for a friendly photo with Piers and co-host Susanna Reid.
This photo was then shared by a Twitter account called @CrossTheBoss76, referring to Morgan as a four-letter expletive followed by the hashtag '#ShalllOpenHimUp' [sp].
Piers shared the offensive post, adding: "I just spoke to the real Kane Finch. He posted this photo to a WhatsApp group & one of his 'friends' then re-posted it (along with others) incl vile abuse to a fake Twitter a/c in his name. Now in hands of @sussex_police.
"Kane seems a nice guy, just needs better friends."
In a subsequent tweet, in which someone asked Piers why it was a police matter, he said: "The real Kane Finch reported it to the police. Nothing to do with me. He is extremely angry & upset about what his friend did to me, @JohnBarrowman & others."
The @CrossTheBoss76, appears to have been deleted.
A Sussex Police spokesman said: "We have received a report of malicious communications having been sent using what appears to be a fake Twitter account by a person in Sussex representing themselves as a third party.
"The people involved have been identified and enquiries are under way to interview them and establish the full circumstances before deciding what further action should be taken."
Police would not specify what town the person was from.