Dann signed for Rovers from Birmingham in the summer for £6 million but has been unable to prevent Blackburn being embroiled in a relegation battle.
The 24-year-old was signed by Steve Kean to partner Chris Samba in the centre of defence, but the latter has expressed his desire to leave the club in January.
According to the Daily Mail, this has led Dann to question his own future with the club, and Liverpool and Arsenal have been alerted to his disquiet.
Both Liverpool and Arsenal were linked with Dann prior to his move to Blackburn, but neither club was reported to have made formal attempt to sign him.
Arsenal instead recruited Per Mertesacker from Werder Bremen on deadline day, having ended their interest in Bolton centre-back Gary Cahill.
Meanwhile, January move from Arsene Wenger for Dann would certainly seem unlikely after the Arsenal boss said he was content with his options in the centre of defence.
Liverpool, likewise, have plenty of options at centre-half, with Daniel Agger and Martin Skrtel forming one of the most formidable pairings in the Barclays Premier League.