Burton broke their transfer record to sign Irvine from Ross County last summer, with the Championship club believed to have paid £330,000 to sign the 24-year-old.
The 13-time Australia international scored 10 times in 42 Championship appearances during the 2016-17 campaign, and according to The Mirror, Brighton want to sign the midfielder for their assault on the Premier League.
Irvine, who has previously been linked with Aston Villa, joined Celtic in 2012, but the Australian only made one first-team appearance for the Hoops before joining Ross County in the summer of 2015.
Brighton will play Premier League football next term after finishing second in last season's Championship table. Burton, meanwhile, ended the campaign in 20th as they narrowly escaped relegation to League One.