Albion could bring Bristol City defender Adam Webster back to Sussex.
But a deal – which would take them through the £20 million barrier for the first time - would NOT be linked to an exit for Lewis Dunk.
The Seagulls are understood to have bid for the 24-year-old centre-back from West Wittering.
At the same time, they are fielding loan enquiries from Championship clubs for defenders Matt Clarke, whose suitors include Derby, and Leon Balogun.
The Argus has been told by a well-placed source that, if Webster were to join Albion, it would have “no direct implications” for Dunk, who has been speculatively linked with a move to Leicester.
Dunk is known to be focused on a new season at Albion, where he is likely to be confirmed as captain, and his club have received no communication from the Foxes about a possible deal.
Albion like Webster and would aim to tie up a deal before the likely last-minute scramble for players ahead of next Thursday afternoon’s deadline.
But they are not in a desperate rush to add to their defensive resources.
City boss Lee Johnson said: “I’m not as confident of keeping him as I was when you guys asked me in America (on a recent pre-season tour), given the level of interest. There have been bids.”
Similarly, Albion are open to Clarke going out on loan in the highly-competitive Championship but do not see it as a priority.
Clarke faces stiff competition for a place after his summer move from League One side Portsmouth.
But Albion would need to be sure they have sufficient defensive resources before letting him go, given head coach Graham Potter includes three at the back among his tactical repertoire.
Albion remain in the running for Brentford striker Neal Maupay but are aware the Bees will not let their star man go until they are confident they can replace him.
Tomer Hemed is still among attacking players at Albion although he is likely to go out on loan.
The club are weighing up loan offers from Championship clubs for young goal-getter Aaron Connolly.
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