The Senegalese forward had a sensational season in Germany last year, finishing as second top scorer in the Bundesliga.
The 26-year-old is understood to have been in England this week to hold talks with Rovers as Freiburg accept their star man is set to leave.
But the German club insist that they will not accept anything less than €15million for him.
Rovers lodged a bid back in May, but that is believed to have been half of what Freiburg wanted, so Steve Kean has returned and upped his offer which, if accepted, would break the club's transfer record.
However, there is strong interest in Cisse, particularly from Eastern Europe with Dynamo Kiev, Lokomotiv Moscow and Zenit St Petersburg all keen and the wages on offer in Russia and Ukraine could hamper Blackburn's bid.
Arsenal, Liverpool and Fulham are also thought to have been keeping tabs on Cisse in recent months.
Rovers are looking to bolster their attacking options, and have also been closely linked with Roma's Mirko Vucinic.
His agent admits to have been in England for talks, but a move within Serie A looks more likely with Juventus strongly linked.
Vucinic's agent Alessandro Lucci said: "I've been to England to take stock of the situation.
"The interest of English clubs in him goes back some time.
"But I've also had meetings with Juventus, where we talked about many players and they asked for information on Vucinic."
Blackburn are also keeping tabs on the situation of former star Roque Santa Cruz at Manchester City after he spent the latter part of last season back on loan at Ewood Park.