The Litex Lovech forward passed a medical at the club last week and had agreed terms on a deal but the Home Office have refused to grant him the necessary paperwork.
The problem is that Popov has not made enough appearances for Bulgaria, having missed several games in the last year due to injury.
The 22-year-old has scored three goals in 15 matches for his country since making his debut in 2007 and is expected to start Friday's Euro 2012 qualifier against England.
The news that he does not qualify for a work permit will come as a major blow to Blackburn as Popov is regarded as a bright prospect for the future and was instrumental in helping Lovech win last season's Bulgarian title.
Rovers were reportedly ready to pay 3million euros (£2.5m) to secure Popov's services and Sam Allardyce had been hopeful of completing the deal.