Wolves and West Ham United have been keeping tabs on the 16-year-old.
The Daily Record says Albion are hoping to beat their Premier League rivals by launching a £275,000 for McArthur.
McArthur has already made a handful of top-team appearances for Scottish Championship side Killie.
The Seagulls' proposal would include a number of add-ons if he was to break into the Brighton first-team.
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