Brighton have received plenty of interest in the vacant manager's job following Oscar Garcia's resignation.
The Seagulls are looking for a new boss for the second summer running after Spaniard Garcia quit on Monday following their failure to reach the play-off final.
Tim Sherwood is currently the bookmakers' favourite for the role having parted company with Tottenham, but Brighton are not commenting on any speculation.
Chief executive Paul Barber told the club's official website: "Most of Monday was spent dealing with Oscar's departure; once we confirmed we had accepted his resignation in the early evening, that of course triggered a number of enquiries to the club about the position.
"We can't divulge any names, and we won't comment on media speculation, but at this stage what I can say is that we have been contacted by some very high-calibre managers and coaches who want to work for Brighton and Hove Albion.
"It's certainly a very good indication of just how far our club has come in a very short period of time."
Meanwhile, the Seagulls have released six players including goalkeeper Tomasz Kuszczak.
The 32-year-old Poland international joined Albion from Manchester United in 2012 and made 89 appearances in two seasons, helping the club reach the play-offs twice.
Fellow keeper Peter Brezovan, injury-plagued striker Will Hoskins, winger Andrea Orlandi and the two 'Spanish Daves', David Lopez and David Rodriguez, have also been told their contracts will not be extended.
But the Seagulls will offer new deals to defenders Inigo Calderon, Bruno and Matt Upson as well as back-up goalkeeper Casper Ankergren, while winger Kazenga LuaLua and youngster Brennan Dickenson will have contract-extension options taken up by the club.
Chairman Tony Bloom said: "On behalf of the club I would like to thank Peter, Will, Tomasz, Andrea, David Lopez and David Rodriguez for their efforts and wish them all the very best for the future.
"I'd also like to thank the players who joined us on loan during the season - Stephen Ward, Keith Andrews, Leroy Lita, Jonathan Obika and Jesse Lingard - for their efforts and excellent professionalism."