The Seagulls have already signed Dutch defender Joel Veltman alongside Wigan Atheltic teenager Jensen Weir and England international Adam Lallana, who signed on a free transfer following the expiration of his Liverpool contract.
But which other deals are the bookies to conclude? Simply scroll down and click through the pages to take a look and what SkyBet and Paddy Power are saying.
All odds correct at the time of writing. Over 18s only. Please gamble responsibly and Be Gamble Aware. www.begambleaware.org.
1. OUT: Shane Duffy
Shane Duffy has been linked with an Amex Stadium exit, with Celtic (5/6), West Ham (2/1), West Brom (7/2), Burnley (13/1), Leeds (18/1) and Fulham (20/1) all tipped to sign the Republic of Ireland international by Paddy Power. Photo: PAUL ELLIS
2. IN: Ainsley Maitland-Niles
The Arsenal attacker - who won the FA Cup with the London club last season is 6/1 on with SkyBet to link up with Graham Potter at the Amex Stadium. Photo: Stuart MacFarlane
3. IN: Ivan Toney
The prolific Peterborough United striker - who started his career at Newcastle United - as been linked with a big-money move to Scottish Premiership champions Celtic. The Seagulls are priced at 12/1 on with SkyBet to sign the attacker. Photo: Luke Walker
4. OUT: Lewis Dunk
SkyBet are tipping Lewis Dunk to sign for Chelsea (1/3), Arsenal (14/1), Manchester United (14/1) and Liverpool (16/1). Photo: Pool