Midfielder Steve Melton has been offered a one-year contract by Albion.
The former Nottingham Forest playmaker, who showed up well on the three-match tour of Ireland last week, was last night weighing up terms offered by Seagulls boss Micky Adams.
Melton, 21, was released by forest at the end of last season and had offers to spend pre-season with Mansfield and Rotherham.
But the chance of teaming up again with Adams, with whom he had worked at the City Ground, persuaded him to head south in pursuit of a decent summer's training at the very least.
Adams revealed: "I've made him an offer and I'm waiting for his reply. It's a good chance for him to come here and show us his worth over a longer period."
Albion are continuing to make enquiries in the hunt for a target man.
But they will have to do without new leftback Nathan Jones for the first two games of the season, including the trip to his former club Southend.
Jones was dismissed in Southend's penultimate game of last season, a 2-0 defeat by Torquay, for deliberate handball in front of goal.
Southend claimed he had cleared the ball with his chest but Albion have now been told the dismissal and subsequent two-match ban will stand.
Jones, player-of-the-year last season for the Essex club, has shown up well as an attacking left back in pre-season.
Adams admitted; "This will alter my pre-season plans slightly.
"It's a blow for us and it's a blow for the boy himself.
"I'm sure he would have liked to have gone back to Southend and got a nice welcome from the fans there."
Jones will join central defender Danny Cullip on the sidelines at Roots Hall on August 12 and at home to Rochdale a week later.
Cullip received a two-game ban after seeing red against Shrewsbury Town at the end of last season.
Adams gives his reserves and youngsters a chance to impress against Chichester City United tonight (7.30). The game takes place at Portfield's old ground in Church Road.
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