Mark Cartwright wants extra time to prove he can fill Albion's goalkeeping gap.
Manager Micky Adams is considering a loan move for the Wrexham shot-stopper, although no decision will be made until he speaks to chairman Dick Knight.
Adams is hunting for an experienced keeper to join Michel Kuipers and Will Packham following the summer switch by last season's No. 1 Mark Walton to Cardiff.
Cartwright joined the Seagulls on trial at the end of last week after Adams faxed every Football League club.
He played in a 5-1 win for an Albion X1 at Selsey on Friday night, then took over from Kuipers for the second half of Saturday's 2-0 friendly win against Sheffield Wednesday at Withdean.
"I had only been back at Wrexham for a week, because I had been training with Exeter for the past month," Cartwright revealed.
"That didn't work out, but hopefully I have done enough here to maybe extend the trial period and see where we go from there.
"I would be very happy to stay, but that is out of my hands."
Chester-born Cartwright started his career at York, then had a year with Stockport before a soccer scholarship in the States.
The 27-year-old signed for Wrexham in March 1994, establishing himself as first choice the season before last when Andy Marriott was sold to Sunderland.
Cartwright had to play second fiddle to Kevin Dearden last term. He has also been with Bury, Bournemouth and Luton this summer.
Adams said: "I'm considering taking him on loan, but I cannot say that's a definite until I speak to the chairman."
Adams was on the phone again yesterday in his relentless pursuit of a new striker for Saturday's first match of the season at Southend.
Albion have already had four bids turned down for a front man during the close season, including former loan capture Bobby Zamora.
"I've made a few phone calls which I will be following up again," Adams said.
"There is money available to strengthen the squad, but clubs are a bit reluctant to deal with the start of the season so close.
"Our chances are receding, but I wouldn't rule it out."
Adams has no complaints about a suspended £25,000 fine from the FA for Albion's poor disciplinary record last season.
"It's fair enough, no more than I expected. Our discipline has to improve and I'm sure it will."
Adams, Knight and chief executive Martin Perry are on the panel for a fans' forum, staged by BBC Southern Counties Radio, at Worthing FC tonight from 6.45pm.
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