Manager Jon Dahl Tomasson wants more options up top and is keen to land Swansea’s versatile forward, 24, whose contract is up after this season.
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Cullen starred for Swansea last season as he bagged eight goals and one assist in 29 Championship outings.
This season, he has endured a slower start to life in the division, having only scored one goal in his first eight league appearances.
Cullen is currently managing a knock that he picked up during the midweek draw with Queens Park Rangers.
Manager Michael Duff is hoping that he will be back for selection soon.
Blackburn are on the lookout for some more firepower as the team has only scored 12 goals so far this season in the league.
However this has not been the case in the Carabao Cup as the team registered massive wins over Harrogate Town and Walsall.
The lack of potency in front of goal has seen the side drop to 14th in the league table despite pushing for a playoff spot last campaign.
The Lancashire-based side lost star striker Ben Brereton Diaz in the summer on a free transfer to LaLiga side Villarreal.
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The Chilean international was a regular contributor of goals in the previous two seasons for the club.
Brereton Diaz scored 36 goals across the last two campaigns but the club were unable to tie him down to a new contract.
Sammie Szmodics has been responsible for providing the club’s goals this season.
The attacking midfielder has netted five goals in all competitions.