Sky Sports understands powerful defender Dann is on the wanted list of all three clubs as they look to bolster their defensive options before the transfer window closes.
Dann, who has attracted the interest of Liverpool and Arsenal in the last 18 months, has impressed in Blackburn's opening two Championship games this season.
The defender's suitors are expected to watch him in action in Blackburn's clash with Doncaster Rovers on Friday night as they step up their interest in Dann.
Blackburn are bracing themselves for offers for the 6ft 5in stopper and have already brought in Matt Kilgallon as cover in expectation of Premier League clubs coming calling for Dann.
Fulham boss Martin Jol is thought to be an admirer of Dann, while Everton chief Roberto Martinez could move for the 26-year-old to add to his centre-back options.
Swansea are keeping tabs on Dann and are ready to move for the former Coventry player should they lose Ashley Williams this summer.
Dann is understood to be keen on a move back to the Premier League and Blackburn are unlikely to stand in his way if they receive a suitable offer as they look to trim their wage bill.
Dann has made 82 appearances for Blackburn since moving to Ewood Park from Birmingham City in 2011.