Former Newcastle United boss Chris Hughton is emerging as favourite for the Brighton job.
The Daily Mail says his appointment as Sami Hyypia's replacement is likely to be confirmed before Saturday's FA Cup tie at Brentford.
Caretaker Nathan Jones is expected to stay on, either as Hughton's assistant or first team coach at Brighton.
Chief executive Paul Barber said: "We've been working down to a shortlist which we're down to now.
"We worked from quite a long list and narrowed it down quickly because of the time of year we're in at the moment.
"We've got a big transfer window coming up and want one or two reinforcements into the squad to boost our squad as it stands and our league position as quickly as possible."