It is claimed that Hearts could receive £350,000 for the 16-year-old, depending on appearances.
Leonard has yet to make a first team appearance for the Edinburgh side, who have handed regular opportunities to teenagers Harry Cochrane - also an Everton target, according to Teamtalk - Jamie Brandon and Lewis Moore this season.
However, the attacking midfielder, who trained with Scotland's Under-21s as a 15-year-old, is not short of admirers, it seems, with Newcastle, Everton and Celtic said to have been lurking.
Should the move go ahead, Leonard would be the latest in a long line of youthful Brighton recruits, which includes 19-year-old ex-Celtic defender Josh Kerr.
Would Newcastle United / Everton / Celtic regret missing out on Leonard to Brighton?