Albion are set to make a decision on the future of Bradley Allen.
The Grimsby striker is coming to the end of a week's trial from Grimsby Town where he is currently out of contract.
Allen, 30, played his third game in Seagulls' colours when he turned out for 62 minutes of a 3-0 friendly win at Crawley Town on Saturday.
The former QPR, Charlton and England under-21 frontman has yet to register a goal for Albion but could offer experience to an area where the senior striker is 21-year-old Bobby Zamora.
Manager Martin Hinshelwood said: "Bradley has got one or two other offers as well. We have just got to look at it and ask, 'Is he what we want?'
"He has done okay in the games we have played. We will have a chat over the weekend and make a decision from there."
Apart from Allen, teenagers Chris McPhee and Daniel Marney have been Albion's only other striking options for the friendlies to date, although Shaun Wilkinson and David Lee have also been used up front with some success.
The good news, though, is Zamora and Gary Hart are on their way back from injuries.
Both were seen limbering up on the pitch before kick-off at Crawley and Hart should figure in a friendly at Bognor tonight after recovering from a broken leg he suffered at Peterborough in the penultimate away game of last season.
Hinshelwood said: "Gary is a week behind the boys in his fitness, which is why we haven't pushed him but we will be looking for him to have some sort of game at Bognor.
"It is only just over a week since Bobby's operation. He will be stepping it up this week with Malcolm (Stuart) and Kim (Eaton) at the training ground and next Monday he will be back in full training with the first team squad."
Hinshelwood has also reiterated his stance over Zamora and has dismissed suggestions that his return to fitness could reignite interest from bigger clubs.
"Bobby is on contract with Brighton and Hove Albion Football Club yet people keep on about it," said Hinshelwood. "Danny Cullip's also on contract here. Until that changes, what is the point of asking whether they are going or not?
"They are here and they want to be here. If it changes, it changes, but at the moment I am pleased they are with this football club and so are they."
Goals from Robbie Pethick, his third in as many pre-season friendlies, Marney and Wilkinson secured a comfortable win at Crawley in front of a crowd of 2,120.
Albion's preparations for First Division football continue this week with tonight's match at Bognor followed by a trip to Gravesend and Northfleet on Wednesday before facing Leyton Orient at Brisbane Road next Saturday.
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