Former Calvin Klein model-turned actor Kutcher, star of 'That 70s Show' and 'Dude Where's My Car', claims that the paper published a quote in an article that he didn't say.
The article quoted him as saying: "She was the hottest actress in Hollywood when I was growing up. I was in love with her when I was 10. Now I'm f****** her."
According to a report in the New York Daily News, Kutcher's representative claims the paper "simply made up" the quotes, and if it "fails to provide Mr Kutcher with an appropriate retraction and apology, he will evaluate all of his legal options".
The report says that Kutcher's claims are backed up by Jane Bussman, the reporter whose name appeared on the article, who accuses the paper of making the quotes up and who is also seeking an apology.
Kutcher has hired top Hollywood lawyer Martin Singer to seek a retraction from the paper.
The Standard has confirmed that it has received a complaint from a Hollywood law firm in the US on behalf of Kutcher.
It said it takes all complaints "very seriously" and is carrying out an urgent investigation into the allegations.
Kutcher and Moore's relationship has attracted a telephone directory's worth of press coverage in recent months, helped by the release of the film 'Charlie's Angels: Full Throttle', in which Moore stars alongside Drew Barrymore, Lucy Liu and Cameron Diaz.
Moore caused ripples when she turned up at the premiere with her children, Kutcher and ex-husband Bruce Willis in tow.
Kutcher has just been confirmed to star alongside Kirstin Dunst in director Cameron Crowe's next movie called 'Elizabethtown'.
The ensemble romantic comedy, written by Crowe, will follow Kutcher and Dunst as they fall for each other at the overly elaborate memorial of a Southern patriarch.
This year, Kutcher has already appeared in 'Just Married' with Brittany Murphy, and his next film, 'The Boss's Daughter' in which he stars alongside Tara Reid, is released in August.
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