They moved for Brown, 28, ahead of Championship rivals Doncaster.
Cardiff have lost Tom Heaton to a groin injury while David Marshall needs elbowsurgery.
Liverpool have looked at Rovers keeper Paul Robinson in case Pepe Reina leaves Anfield in the summer.
A buyer would have to meet the ?20m release clause in Reina's contract.
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Explore more:People: David Marshall, Paul Robinson, Pepe Reina Places: Liverpool, Cardiff