Allardyce, who has spent the summer searching for forwards, has previously confirmed his interest in Kalinic and he now appears to have got his man.
The player's representative, Tomislav Erceg, has backed up the Croatian club's claims a deal has been agreed between the clubs and all that is now required is to obtain a work permit.
"It is finished, the transfer is completed. Now all Nikola needs is a work permit, which shouldn't be problem," Erceg told Sportske novosti.
Reports say Kalinic has signed a four-year deal with Rovers, who have confirmed that Di Santo has joined the club on loan from Chelsea until January.
Rovers will then have first option on extending the deal providing Chelsea are willing to let him stay on loan for the remaining months of the season.
Di Santo could make his first appearance for Blackburn in Wednesday's home friendly against Hibernian.
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