McArthur and McCarthy have been linked with a number of clubs
Hamilton Academical chairman Ronnie MacDonald is determined to hold on to his young squad after rebuffing interest in four of his star men.
"The club has received approaches for four of our players, but none of them are for sale this season," he told BBC Scotland on Tuesday.
Accies have impressed on their return to Scotland's top flight this season.
And midfielders James McCarthy and James McArthur, plus defender Brian Easton, have been attracting interest.
MacDonald refused to name the four players for whom he had rejected approaches.
But McCarthy, who made his first-team debut two years ago aged 16, has previously had talks with Celtic, Chelsea, Liverpool, Rangers and Reading before deciding to continue his development at New Douglas Park.
Easton, a 20-year-old who has previously been linked with West Ham United, and the 21-year-old McArthur, are also products of Hamilton's youth system.
MacDonald said that, rather than losing players, he was hopeful of adding a couple of new faces to the squad before the closure of the January transfer window.
The departure of several fringe players and the collapse of the deal to sign former Scunthorpe defender Izzy Iriekpen, who has decided to join Bristol City instead, means there are funds available.
MacDonald, though, stressed that the club would prefer to promote from their youth ranks - and that Accies were gaining a reputation around Europe for giving their emerging talent a chance to shine in the first team.
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