Coppell joined the Albion last October, has been offered a new contract at the Withdean.
He took over from Martin Hinshelwood, who was sacked after the Seagulls took just four points from their first 14 games.
Albion chairman Dick Knight said: "Steve has done a wonderful job in the time he has been here, and the board and I want him to lead this club forward.
"Steve wants time to consider the offer we've made. That is the way he wants to play it and I respect that.
"It's a good offer, because we want him to stay. I will be continuing the discussions with Steve, after he has had time to digest the details," Knight told the club's website.
Sir Steve has talked in the past about the lack of Scouts at the Club, that he finds it unbelievable that there is no scout employed by the Club at all.
He would need a decent budget for the playing side, to be able to retain the likes of Beasant, Rodger & Blackwell, as well as strengthening the side for the push to get straight back into the First Division.
That budget for Scouting & playing staff may well be dependant on a decent offer coming in for Bobby Zamora. The statement by Bobby's agent that he would only leave Brighton for the Premiershoip may make that transfer more unlikely, now that the proven premiership strikers such as Defoe, Kanoute & Phillips are all available from Relegated West Ham & Sunderland.
On the other hand, what other jobs are there that Coppell could take, he doesn't want to be left in Footballs Managerial wilderness.
We think he'll stay with the Albion.