The Scottish Sun suggest that Albion sent someone to Dundee's game against Motherwell at the weekend to have a look at the 25-year-old, as Chris Hughton looks to strengthen the club's promotion bid during the January transfer window.
Similarly however, Mark Warburton has reportedly been hoping that Stewart - who was released by Rangers as a youngster - could enhance the Gers' own push for a top flight return.
Although the Seagulls remain at the top of the Championship, the division remains congested, with the three teams below all within four points of Hughton's side despite their unbeaten start.
Meanwhile, Rangers' failure to beat Morton on Saturday was not punished, as the Gers' nearest challengers Hibernian were also only able to draw their game against Falkirk, leaving the gap at the top at three points..
With both sides' precarious positions at the top of their respective tables, having a striker of Stewart's prowess would certainly increase their chances of remaining at the top of the pile come the end of the season.
Although Stewart has just five goals in the Scottish Premiership this campaign, his 15 goals in all competitions last term highlighted just how dangerous he can be.