Albion chairman Dick Knight has pledged to have a new manager in place by next Wednesday.
He refuses to be rushed into an appointment for Saturday's home game against Stockport but says the interview process is nearing completion.
Another candidate who Knight is interested in has come forward since last Saturday, when he revealed to The Argus he was down to a shortlist of four.
The list is thought to include Oldham chief Iain Dowie and ex-Southampton manager Stuart Gray, as well as caretaker Bob Booker.
A surprise contender could be Torquay's head coach Leroy Rosenior. Rosenior, who worked with former Albion captain Danny Wilson at Bristol City, has a rolling one-year contract with the Third Division club.
Knight, although refusing to discuss names, said: "There are people working at clubs without contracts and some with rolling contracts.
"They are both open-ended and free to leave the club if they wish."
Booker will be in charge again against Stockport, but his hopes of landing the job have been wrecked by defeats against Bournemouth and Brentford.
Knight said: "By next Wednesday I expect to have the Brighton manager's position resolved.
"I am not panicking because we have lost two games on the trot. The fact is we are still near the top of the League and people should remember that."
Knight believes uncertainty created by Steve Coppell's departure was responsible for the below-par performances in last Saturday's 1-0 defeat at Bournemouth and Tuesday's 4-0 drubbing at Brentford.
He said: "The past few days have shown that a successful team losing its manager through his own choice is bound to affect the players, subconsciously or otherwise.
"It happened to Reading and it's happening to us. We must put things right quickly. From the long list of applicants, my interviewing and evaluation of the main candidates for the job is almost complete.
"Meanwhile, we have strong characters in our squad. The players will want to put the last two performances behind them and show what they are really capable of against Stockport."
Albion go into the game in second place. Plymouth are the new leaders on goal difference after a 3-1 victory at Sheffield Wednesday on Wednesday night.
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