The commanding 6ft1 centre-half has less than a year left on his current deal with the English Championship side.
Brown has already gained experience of playing in the Scottish Premiership with Livingston, spending three separate loan spells with the West Lothian outfit where he made a combined total of 34 appearances.
His most recent stint north of the border was cut short in February after a string of impressive displays saw him recalled by Bluebirds manager Mick McCarthy.
The 23-year-old scored and assisted a goal during Livi’s 2-2 draw against Celtic in January and he became a regular towards the end of last season, helping Cardiff to an eight-placed finish.
It appears the Welsh side are reluctant to sell Brown who was also attracting interest from Middlesbrough over the summer.
However, the Northern Ireland international, who has four caps to his name, may view the lure of playing for one of Glasgow’s Old Firm giants too good to turn down.
According to GiveMeSport, Rangers are eyeing up a potential pre-contract deal for the defender in January with a view to him joining on a free transfer next summer.
During his time at Livingston, manager David Martindale outlined Brown’s footballing intelligence as one of his biggest assets.
He stated: “Ciaron has got a very good football brain. When I ask him to do a job, he knows what to do and nine times out of ten he will make the right decision.”