The Leicester Mercury says the Foxes have taken a step closer to signing Campbell from Cardiff after triggering a release clause in his contract.
The 26-year-old has a relegation clause which allows him to speak to other clubs if they bid £800,000.
However, no talks were scheduled with the player's representatives for this week.
Bluebirds chairman Mehmet Dalman said: "We have to allow Fraizer to make his own decision, but hopefully he can stay."
For the big stories and the banter follow us on Twitter: @tribalfootball