Albion have turned down a £5 million bid from Championship rivals Fulham for Lewis Dunk.
The latest offer, the third made by Fulham for the centre-half, was rejected yesterday The Argus understands.
The Seagulls remain intent on trying to keep hold of Dunk.
They have been actively involved in trying to improve his personal terms after he signed a new four-year deal 12 months ago.
But they could be fighting a losing battle in the face of the persistent interest of Fulham, who benefit from parachute payments following relegation from the Premier League two seasons ago, and an anticipated bid from Newcastle United.
The North-East giants have yet to make an official offer for Dunk, although the Argus understands they have indicated strong interest.
Albion have made provisions for the growing possibility of Dunk departing before the transfer window closes.
They completed the capture of Shrewsbury prospect Connor Goldson last night after buying German centre-half Uwe Huenemeier from Paderborn last week.
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