Reports indicate new Rovers boss Paul Ince has tabled a £3million bid for Davis in a bid to lure him to Ewood Park.
The 23-year-old spent the second half of last season on loan at Ibrox from Craven Cottage, making 26 appearances in all competitions as the Gers narrowly missed out on the Scottish Premier League title and the UEFA Cup.
Speaking on Friday, Rangers boss Walter Smith remained hopeful he could strike a deal with Fulham for Davis.
However, Blackburn are not the only club interested in snatching Davis.
Middlesbrough, Sunderland and Bolton have also been monitoring the situation and could yet enter the chase for the former Aston Villa man.