Cardiff manager Neil Warnock
And Warnock, the former Sheffield United manager, is quoted as saying: "[£3 million] wouldn't even buy one of Morrison's legs."
According to Wales Online, Cardiff believe that selling Morrison would "send out the wrong signals" ahead of a planned promotion push.
And another concern for the Bluebirds is the future of another central defender, Bruno Ecuele-Manga, whose contract with them expires at the end of this month.
Cardiff City defender Bruno Ecuele Manga [left]
It remains to be seen whether Wednesday, who have been defeated in each of the last two Championship play-off campaigns, will continue their interest in Morrison, who scored four league goals and created another eight this past season.
Owls boss Carlos Carvalhal is keen to add at least one new centre-back this summer and is considering bids for Grant Hanley and Daniel Ayala, of Newcastle United and Middlesbrough respectively, according to the Sheffield Star.
How much should Sheffield Wednesday pay for Morrison?
Sheffield Wednesday head coach Carlos Carvalhal [left] with owner Dejphon Chansiri