The Seagulls are one of a number of clubs reportedly chasing the centre-back's signature.
The 24-year-old has been attracting plenty of attention this summer following an excellent season at Ewood Park which saw him earn a place in the Republic of Ireland's squad for the European Championships.
The Irish Sun reports that both Wolves and Celtic have been monitoring the defender's situation, though Rovers boss Owen Coyle recently insisted that the latter had not made a move following intense speculation.
Perhaps fearing that another interested club will swoop in, Brighton have seemingly cemented their interest with a bid for the former Everton man as they look to build on the promise they showed last season.
Brighton manager Chris Hughton
Chris Hughton's men finished the regular campaign third in the table - having only missed out on automatic-promotion on the final day - but the disappointment of coming so close appeared to linger as they were beaten in the play-off semi-final by Sheffield Wednesday.
But with Lewis Dunk being linked with a Premier League switch (via Express and Star), Hughton will know that getting an adequate replacement in could be crucial to their promotion hopes this time around.