The Sun says the Seagulls are desperate for a finisher and have been sending top spies to watch the former Newcastle prospect in action recently.
West Ham are keen on Armstrong but reluctant to pay the asking price of £25million.
Brighton may go close as he fits the bill — and Albion have struggled for goals this term.
Armstrong, 24, is a more natural finisher than anyone they have and is also young and English.
His wages would not be too high for them, either.
Rovers are slowly becoming resigned to selling him this summer.