Hello and welcome to the forums!
This is caused by the difference in white balance between your ambient light and the television. I am assuming you are filming indoors with tungsten lighting, which means the white balance of your light is at a yellower point than that of your television. Your camera will automatically adjust to match the white balance of the ambient light, leaving the television looking blue.
In a television studio, the lighting will be of the same white balance as the TV monitors you can see. You have a few options here:
- Get hold of some studio lighting that is closer to daylight white balance
- Adjust the white balance of the TV screen to match your ambient lighting. If this is not possible you may be able to use a computer monitor in its place
- Use as much daylight as possible. You haven't said what specifically you're filming so it's hard to know whether this is practical