British media reports say the marriage is in trouble.
Representatives of the couple declined to comment but said a statement is expected at some point on Wednesday.
According to the Daily Mirror, the 63-year-old former Beatle is asking Mills, 38, for a formal trial separation, because of many bitter fights.
The paper quotes an unidentified source as saying: "Paul hasn't come to this decision lightly, but felt things couldn't carry on as they were."
McCartney is also quoted as having told a friend: "We really can't go on like this. Enough is enough."
Mills just last week, according to the BBC, soft-pedaled reports that she and McCartney were living at separate addresses, telling a newspaper reporter at that time: "It's hilarious. Of course we are together... Paul and I are still very much together. Paul and I are together 100%."
The BBC says now that it has learned the couple does plan to separate.
There has been no announcement from either McCartney or Mills, who have a two-year-old daughter, Beatrice.
They married in 2002, in a storybook ceremony at an Irish castle, four years after McCartney lost his first wife, Linda, to cancer.
Mills, a former model who threw herself into charitable activity after losing a leg in an accident, first met McCartney at a fundraiser and has had his vocal support in her chosen causes – artificial limbs for amputees and the campaign to remove and ban landmines, promoted on his most recent concert tour.
She has responded in kind when it comes to public support of issues McCartney cares about, and in March she accompanied him to an ice floe off the coast of Canada, to take a stand against the annual fur traders' hunt of baby seals.
The Mirror reports Mills and Beatrice remained at the couple's home in England recently while McCartney went to France to decide what to do about their situation.