Reports from the League 1 club suggest Robinson, 34, has turned down the chance to take over the vacant hotseat at the Championship club.
At the same time, Brighton chief executive Paul Barber says caretaker Nathan Jones is being considered for the permanent managerial post with their number one target out of the frame
The 41-year-old, who was first-team coach under Sami Hyypia before the Finn's resignation on Monday, oversaw the 2-2 Boxing Day draw with Reading.
"It's absolutely right we'd consider him as part of the process and we have told him that," Barber told BBC Sussex.
"At the same time his immediate focus is preparing the team for Fulham."
Hyypia, 41, quit as manager after one win in 18 league games.
Albion chairman Tony Bloom has arrived back from Australia and Barber confirmed the club had completed a shortlist and were already talking to potential replacements.
Bloom reiterated the need for a swift appointment with the start of the January transfer window only days away.
He has been impressed by the passion shown by Jones, who played for Albion between 2000 and 2005.
"Nathan has history here as a player and is a very passionate guy, a very committed professional coach who would dearly love to step up to the top job," added Bloom.
Former Crystal Palace and Stoke manager Tony Pulis, ex-Spurs head coach Tim Sherwood and former Norwich boss Chris Hughton have also been linked with the post.