The celebrity couple spent their recent sixth wedding anniversary (September 24) apart sparking rumours that they have broken up, Radar Online claims.
In addition, Moore has posted a series of cryptic tweets over the past month.
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On September 23 - the day before Kutcher and Moore's anniversary - Moore posted a quote from Greek philosopher Epictetus reading: "When we are offended at any man's fault, turn to yourself and study your own failings. Then you will forget your anger."
A few days later, she posted a picture of herself accompanied by the words: "I see through you."
Representatives for the two actors have yet to respond to the speculation.
Last year, Kutcher was rumoured to have cheated on Moore after being spotted "kissing and groping" another woman in Los Angeles.
However, the Two and a Half Men star denied the reports, with his lawyer declaring that the claims were lies.
