Reports suggest that Saints boss Nigel Adkins is eyeing the centre-half to boost his defensive options ahead of the start of the Premier League season.
The 25-year-old joined Rovers after suffering relegation with Birmingham in the August transfer deadline day last season for £6m, before dropping down into the Championship with his new club just 10 months later.
And Adkins is hoping the lure of flight football will be enough to entice Dann from the second-tier club as the Saints look to negotiate a fee of between £3-4m for the England Under-21 international.
The report add that the centre-back has had to take a pay-cut side Steve Kean’s since relegated and only an offer similar to that of his old wages would seem him move from the Lancashire club.
If Dann completes a move to Southampton he will be their fifth signing of the summer joining Jay Rodriguez, Steven Davis, Nathaniel Clyne and Paulo Gazzaniga at St Mary’s.