Seagulls manager Chris Hughton is believed to be keen to add top-level experience to his fledgling squad, and 10-year veteran Lucas would be a prime candidate if that was the case.
But according to a report from the Daily Record, Hughton could be forced to do battle with former Liverpool manager Brendan Rodgers.
They claim that “Rodgers is scanning the globe hunting fresh faces to boost his squad.”
They incorrectly suggest that Lucas will be able to leave Liverpool on a free transfer this summer, despite it having been revealed he has one year left on his current deal.
It could well be that Lucas opts to depart at the end of the season, with his fate seemingly in his own hands ahead of talks with Jurgen Klopp.
But whether Celtic will be his preferred destination is questionable, as are claims of Rodgers’ interest.
Lucas made 98 appearances under Rodgers at Liverpool, averaging 72 minutes on the field per outing, taking up a regular role in the Reds’ midfield.
But Rodgers came close to selling Lucas on a number of occasions, most notably when Besiktas made an approach to sign him on loan at the start of the 2015/16 campaign.
Rodgers does have previous when it comes to signing his former players, of course, having brought Joe Allen with him from Swansea City when he joined the Reds in 2012.
He also moved to sign Kolo Toure on a free transfer last summer, with the Ivorian going on to lift his third league title with the Scottish Premiership this season.
Celtic could offer Lucas the chance to play in the Champions League, as he did under Rodgers in 2014/15, which he would not be able to do with Brighton.
But with Lucas confident he still has a lot left to offer at the top level, moving across the border would arguably be a step down.