The 22-year-old has been on trial at Ewood Park but Rovers denied claims by the player's club Litex Lovech last week that a deal had already been completed.
Allardyce said: 'We had a little look at him and we are in tentative negotiations.
Popping in? Blackburn boss Sam Allardyce admits he is interested in Ivelin Popov but says negotiations are far from complete
'I am not so sure what the total outcome is in terms of price, but he is an interesting player.
'He is a very good young prospect but whether all the numbers stand up is another matter.'
Allardyce is anxious to recruit more firepower to supplement Niko Kalinic before the summer transfer window closes.
He added: 'We are trying to get players in and we all know what position we want it to be.
'I don't want to be doing anything after Friday of this week - I don't want to be panicking or judging the market in the last couple of days of the window.
'It is unhealthy doing it like that and you could very easily make mistakes.'
Former Manchester City and Portsmouth forward Benjani Mwaruwari has also been training with the Lancashire outfit this month and Allardyce will give consideration to a deal.
The Zimbabwe international, 32, was released by City at the end of last season.
Allardyce said: 'Benji is training with us. We'll see where we are when that training finishes in the middle of the week and make a decision there.' Blackburn insist no deal is done for £1.5m Bulgarian striker Popov. yet!Foster: Blackburn's long-ball tactics and giants are the stuff of nightmares Birmingham 2 Blackburn 1: Gardner digs out the points for McLeishBLACKBURN ROVERS FC